CN201331862Y - Rotating vector demonstration instrument - Google Patents

Abstract

The utility model is a rotating vector demonstration instrument, which includes a box body, a demonstration panel, a backboard and an electronic controller, and is mainly composed of two groups of bulbs on the demonstration panel, the rotation vector diagram and the vibration curve diagram, and the electronic controller arranged in the box. , during the demonstration, under the control of the electronic controller made of integrated circuits, the bulbs at the corresponding points on the circumference, sine curve and projection line are respectively lit in sequence, and the projection and demonstration of the rotation vector endpoint on the vertical coordinate axis can be demonstrated. The vibration curve, the relationship between the rotation vector method and the vibration curve method for demonstrating simple harmonic vibration are clear at a glance and easy to learn and understand; the positive effect of the utility model is that the demonstration instrument has stable performance, good effect, long life, simple structure and convenient operation , is a demonstration instrument with intuitive image, good demonstration effect and convenient teaching.

Description

A rotating vector demonstrator

【Technical field】

The utility model relates to the technical field of teaching experiment demonstration instruments, in particular to a rotating vector demonstration instrument in physics teaching.

【Background technique】

When an object moves, if the displacement (or angular displacement) away from the equilibrium position changes with time according to the law of cosine function, this kind of motion is called simple harmonic vibration, and its mathematical expression is:

x＝Acos(ωt+φ) ①

In the formula, A is the amplitude of the vibration, ω is the angular frequency of the vibration, t is any time, and φ is the initial phase of the vibration.

If the three characteristic quantities describing the simple harmonic vibration are known, the complete expression of the vibration can be written, and the curve of the vibration can be drawn, and the characteristics of the simple harmonic vibration can be mastered. This method of studying simple harmonic vibration It is called the vibration curve representation.

There is a simple correspondence between simple harmonic motion and uniform circular motion. Let the mass point P rotate counterclockwise at a uniform angular velocity ω on a circle with a radius of A, take the center O as the origin, and take the Cartesian coordinate system xoy; let the position vector of the mass point P pass through the position where the angle between the x-axis and the x-axis is φ Timing, then at any time t, the angle ωt+φ between the bit vector and the x-axis, and the projection of the particle on the x-axis is:

x＝Acos(ωt+φ) ②

This formula is the same as the definition formula ① of simple harmonic vibration.

It can be seen from this that the projected motion of a mass point in uniform circular motion on a certain diameter (taken as the x-axis) is simple harmonic vibration, the angular velocity of circular motion is the angular frequency of simple harmonic vibration, and the radius is equal to the amplitude of simple harmonic vibration. The angle between the position vector and the x-axis of a mass point in circular motion at all times is the initial phase of simple harmonic vibration.

It can be seen that there is a one-to-one correspondence between uniform circular motion and simple harmonic vibration. Therefore, the simple harmonic vibration can often be studied with the help of uniform circular motion to simplify the calculation, and the corresponding circle is called the reference circle. This representation of simple harmonic motion is called the vector diagram method (rotation vector method).

The problem of simple harmonic vibration is mentioned in the physics teaching of middle school and university, and demonstration and experiment of simple harmonic vibration are required. At present, spring vibrators are usually used in such demonstrations and experiments. However, the demonstration of this teaching instrument can only allow students to observe the phenomenon of simple harmonic vibration, and cannot correspond to the relationship between uniform circular motion and simple harmonic vibration, and cannot demonstrate rotation. The projection of the vector endpoints on the vertical coordinate axis cannot demonstrate the vibration curve, nor can it demonstrate the relationship between the rotation vector method and the vibration curve method of simple harmonic vibration. Therefore, its teaching demonstration effect is very limited.

【Content of utility model】

The purpose of the utility model is to overcome the deficiencies of the prior art, and provide a demonstration instrument for physics teaching with simple structure, portability, intuitive image and good demonstration effect, which is convenient for teaching and improving students' understanding.

In order to achieve the above object, the technical scheme that the utility model takes is:

A kind of rotary vector demonstrator, including box body, demonstration panel, backboard and electronic controller, it is characterized in that circle, sinusoidal curve and projection line are drawn on the demonstration panel, 12 small holes are evenly drilled on the circumference, in Drill 13 small holes on the corresponding points of the sinusoidal curve, drill 7 small holes on the corresponding points of the projection line, install a 6V small light bulb in each small hole, and use wires and electronic control for the small light bulbs on the three corresponding points Connect the controller; set the power switch, automatic/manual selection button, reset switch, pause switch and single pulse switch on the demonstration panel; set the electronic controller, electronic components and connecting wires in the box body 1, and the electronic controller is composed of Made of integrated circuits, mainly composed of power supply, clock, logic control circuit, and output driver; a power socket is set on the backplane.

Optionally, the logic control circuit includes a counting integrated block, a decoding integrated block, two double D flip-flops, and 12 two-input NAND integrated blocks.

Optionally, the counting integrated block is a 74LS92 counter, the decoding integrated block is a 74LS154 decoder, the double D flip-flop is a 74LS74, and the two-input NAND gate integrated block is a 74LS00.

When the rotation vector rotates for the first round at the initial position, the light bulb at the starting point of the circle on the demo panel and the light bulb at the 0° point of the sinusoidal curve light up together, while the light bulb at the 360° point of the sinusoidal curve does not light up; when the rotation vector rotates one circle back When the initial position is reached, the bulbs on the starting point of the circle and the bulbs on the 0° and 360° points of the sine curve are all lit, and the next vibration cycle starts.

When the pause switch is pressed once, the light position remains unchanged, and when it is pressed again, the counter and the decoder start to work.

When the auto/manual selection button is in the "manual" position, the basic RS flip-flop composed of IC ₂ generates a single pulse, press the single pulse switch once, a pulse is generated, and the light moves forward one position.

The power supply of the electronic controller is the +5V power supply for the electronic controller and the AC power supply for the 6V small light bulb.

A rotation vector demonstration instrument of the utility model is designed according to the basic principle that simple harmonic vibration can be represented by a rotation vector. Projection of vector endpoints on the vertical axis; demonstration of vibration curves; demonstration of the relationship between the rotation vector method and the vibration curve method for simple harmonic vibration. When demonstrating the rotation vector representation method and vibration curve representation method of simple harmonic vibration, under the control of the electronic controller, the two groups of bulbs on the rotation vector diagram and vibration curve diagram are respectively lit in sequence, and the two methods are compared. Make it clear at a glance, easy to learn and understand.

The positive effect of a kind of rotating vector demonstrator of the utility model is:

(1) By controlling the bulbs at the corresponding points on the circumference, sine curve and projection line to light up in order, the projection of the rotation vector endpoint on the vertical coordinate axis can be demonstrated, the vibration curve can be demonstrated, and the rotation vector method and vibration of simple harmonic vibration can be demonstrated The relationship between curve methods.

(2) The electronic controller is made of an integrated circuit, so that the demonstration instrument has stable performance, long life, good effect and convenient operation.

(3) Provide a demonstration instrument with simple and portable structure, clear and intuitive image, good demonstration effect and convenient teaching.

【Description of drawings】

Accompanying drawing 1 is the panel structure schematic diagram of a kind of rotating vector demonstrator of the present utility model;

Accompanying drawing 2 is the back structure schematic diagram of a kind of rotating vector demonstration instrument of the present utility model;

Accompanying drawing 3 is the circuit diagram of a kind of rotating vector demonstration instrument of the present utility model.

The labels in the figure are:

1. Cabinet, 2. Demonstration panel, 3. Backplane, 4. Circle, 5. Sinusoidal curve, 6. Projection line, 7. Small hole, 8. Power switch, 9. Auto/manual selection button, 10. Clear Zero switch, 11, pause switch, 12, single pulse switch, 13, power socket.

【Detailed ways】

A specific embodiment of a rotating vector demonstrator of the present utility model is given below in conjunction with the accompanying drawings.

See attached drawing 1.

A rotating vector demonstrator, including a box 1, a demonstration panel 2, a back panel 3 and an electronic controller. For the convenience of teaching, the box used is 100cm long, 10cm wide, and 40cm high, and can be made of wood or plexiglass Production; a circle 4, a sinusoidal curve 5 and a projection line 6 are arranged on the demonstration panel 2, 12 small holes 7 are drilled evenly on the circumference, and 13 small holes 7 are drilled on the corresponding points of the sinusoidal curve 5, Drill 7 apertures 7 on the corresponding point of projection line 6, a 6V bulb is installed in each aperture 7, and the bulbs on the three corresponding points are connected with wires and electronic controllers.

In the lower right corner of the demonstration panel 2, a power switch 8, an automatic/manual selection button 9, a reset switch 10, a pause switch 11 and a single pulse switch 12 are set. When the pause switch 11 is pressed once, the light position remains unchanged, and when pressed again, the counter and the decoder start to work. When the automatic/manual selection button 9 is in the "manual" position, the basic RS trigger composed of IC ₂ generates a single pulse, press the single pulse switch 12 once, a pulse is generated, and the light moves forward by one position.

An electronic controller, electronic components and connecting wires are arranged in the box body 1, and the electronic controller is made of an integrated circuit, mainly composed of a power supply, a clock, a logic control circuit, and an output driver. The logic control circuit includes a counting integrated block, a decoding integrated block, two double D flip-flops, and 12 two-input NAND integrated blocks. The counting integrated block is a 74LS92 counter, the decoding integrated block is a 74LS154 decoder, the double D flip-flop is a 74LS74, and the two-input NAND integrated block is a 74LS00.

See attached drawing 2.

A power socket 13 is arranged on the lower right side of the back panel 3 of the box body 1 .

See attached drawing 3.

The utility model transforms the 220 volt mains power through a transformer, and after rectification, filtering, and IC ₈ voltage stabilization, one output stable +5 volt voltage provides power for the electronic controller, and the other output provides power for the 6V small light bulb on the demonstration panel. AC power.

Clock of the utility model: the clock circuit is composed of two parts. When the automatic/manual selection button 9 is in the "automatic" position, a self-excited multivibrator composed of IC ₁ and peripheral components W ₁ , R ₁ , and C ₁ generates a clock signal, changing _W1 can change the frequency of the clock signal, that is, can change the speed at which the lights move.

When the automatic/manual selection button 9 is in the "manual" position, the basic RS trigger composed of IC ₂ generates a single pulse, press K ₃ once, a pulse is generated, and the light moves forward one position.

The logic control circuit of the utility model is mainly composed of main logic circuits IC ₅ , IC ₆ and control logic circuits IC ₂ , IC ₃ , IC ₄ , and IC ₇ . IC ₅ is a binary counter, IC ₆ is a four-wire to sixteen-wire decoder, IC ₃ is a double D flip-flop, IC ₂ , IC ₄ , and IC ₇ are four-two input NAND gates.

When the power is turned on, the differential circuit composed of R ₇ C ₃ generates a positive pulse to act on the CR terminal of IC ₅ to reset IC ₅ , and its output terminals Q _A ~ Q _D are all low potentials, and the decoder IC ₆ Y ₀ outputs a low potential, and Y ₁ to Y ₁₅ output a high potential. At the same time, the integral circuit composed of R ₆ and C ₂ generates a negative pulse to act on the R terminal of IC ₂ , the double D flip-flop resets, 2Q of IC ₃ is high potential, 1Q is low potential. From the counting and decoding truth table of IC ₅ and IC ₆ , it can be seen that when the clock CP is input, the counter IC ₅ counts and codes, and after decoding by the decoder IC ₆ , Y ₀ ~Y ₅ , Y ₈ ~Y ₁₃ sequentially output low potentials, so that the drive circuits connected to Y ₀ -Y ₅ , Y ₈ -Y ₁₃ drive the bulbs to light up sequentially. The starting point on the 4 circumferences of the circle is corresponding to the 0 ° position on the sinusoidal curve 5, and gets back to this point after one revolution, but then reaches the position of 360 ° on the sinusoidal curve 5. For this reason, when the utility model allows the rotation vector to start the first rotation at the initial position, the light bulb at the starting point of the circle 4 and the light bulb at the 0° point on the sinusoidal curve 5 light up together, while the light bulb on the sinusoidal curve 5360° does not light up , when the rotation vector rotates one circle and returns to the initial position, the bulbs at the starting point of the circle 4 and the bulbs at 0° and 360° on the sinusoidal curve 5 are all lit, indicating that the next vibration cycle begins.

In order to achieve the above-mentioned demonstration effect, the utility model connects the light bulb at the starting point of the circle 4 and the light bulb at the 0° point on the sinusoidal curve 5 in parallel, one of the _Y1 output ends of IC ₆ is connected to the drive circuit, and the other is connected to the 1CK of IC ₃ One of the Y ₀ output terminals is connected to the drive circuit, the other is connected to the input terminal of an inverter composed of a NAND gate of IC ₄ , and the output terminal of the inverter is connected to an input terminal of another NAND gate of IC ₄ , and the NAND gate The other input terminal of the gate is connected to the 1Q terminal of IC ₃ , and the output terminal is connected to the driving circuit to drive the 360° light bulb on the sinusoidal curve 5 .

When the power is turned on, 1Q of IC ₃ is at low potential, and the NAND gate is blocked. When y ₀ outputs low potential, the light bulb on the 360° point of the sinusoidal curve does not light up. When Y ₀ changes from low potential to high potential, IC ₃ The 1Q of Y turns over, changes from low potential to high potential and remains unchanged (unless the NAND gate is turned on when the power is turned on); when Y ₀ outputs low potential again, the light bulb on the sinusoidal curve 5360° becomes brighter to achieve the desired demonstration effect.

Since Y ₁ and Y ₁₃ , Y ₂ and Y ₁₂ , Y ₃ and Y ₁₁ , Y ₄ and Y ₁₀ , Y ₅ and Y ₉ cannot output low potential at the same time, connect them to IC ₄ , IC ₇ and non- The two input terminals of the gate, as long as one of the two input terminals of the IC ₄ and IC ₇ NAND gates is a low potential, the output of the NAND gate is a high potential. The utility model drives the bulb on the resonant vibration connection through the drive circuit, so that no matter which of the two corresponding bulbs on the 4 circumferences of the circle is bright, the bulbs on the resonant vibration connection are all bright.

After turning on the power, 2Q of IC ₃ is at high potential, 2Q is connected to 3A of IC ₄ , so that the counting pulse can be connected to the counting state through IC ₄ and 2D, when the pause switch K ₄ is pressed once, the D flip-flop turns over, and 2Q is activated by The high potential becomes low potential, 3Y of IC ₄ is blocked, and the counting pulse cannot pass through, so that the state of IC ₅ and IC ₆ remains unchanged, and the position of the light also remains unchanged. When the pause switch _K4 is pressed again, 2Q changes from low potential to high potential, and the counter and decoder start to work. Press the reset switch K ₅ once, the counter and the double D flip-flops are reset, and the light starts to move from the initial position.

Drive circuit

The signals output from 2Y of IC ₄ and IC ₆ are sent to the base of the (PNP) transistor after passing through each current-limiting resistor, and the signals output from 3Y and IC ₇ of IC ₄ are sent to the (NPN) transistor after passing through each current-limiting resistor The base, the triode drives the bidirectional thyristor to conduct through a 75 ohm resistor.

Component selection

Since the bidirectional thyristor load is very small, you can choose one with a small current capacity, and the values and models of other components are marked on the diagram.

To connect the electronic controller of a kind of rotating vector demonstration instrument of the present utility model with each bulb of the demonstration panel 2, as long as the bulbs on the demonstration panel 2 are connected to the corresponding silicon controlled rectifiers of the electronic controller, set on the demonstration panel 2 Power switch 8, automatic/manual selection button 9, reset switch 10, pause switch 11 (see accompanying drawing 1); Power socket 13 (see accompanying drawing 2) is set on the backboard 3.

Claims (6)

1. A rotary vector demonstrator, comprising a casing, a demo panel, a backboard and an electronic controller, characterized in that, on the demo panel, draw a circle, a sinusoidal curve and a projection line, and drill 12 small holes evenly on the circumference , Drill 13 small holes on the corresponding points of the sinusoidal curve, drill 7 small holes on the corresponding points of the projection line, install a 6V small bulb in each small hole, and use wires and wires for the small bulbs on the three corresponding points Connect the electronic controller; set the power switch, automatic/manual selection button, reset switch, pause switch and single pulse switch on the demonstration panel; set the electronic controller, electronic components and connecting wires in the box body 1, and electronic control The device is made of integrated circuits, mainly composed of power supply, clock, logic control circuit, and output driver; a power socket is set on the backplane. 2. A rotating vector demonstrator according to claim 1, wherein the logic control circuit includes a counting integrated block, a decoding integrated block, two double D flip-flops, 12 binary Input NAND integrated block. 3. A rotating vector demonstrator according to claim 2, characterized in that, the counting integrated block is a 74LS92 counter, the decoding integrated block is a 74LS154 decoder, and the double D flip-flop is A 74LS74, and a two-input NAND gate integrated block is a 74LS00. 4. A rotating vector demonstrator according to claim 1, characterized in that the starting point on the circle corresponds to the 0° position on the sine curve, and the light bulb at the starting point of the circle corresponds to the light bulb at the 0° point on the sine curve In parallel connection, one of the Y ₁ output terminals of IC ₆ is connected to the drive circuit, and the other is connected to the 1CK terminal of IC ₃ ; one of the Y ₀ output terminals is connected to the drive circuit, and the other is connected to the inverter input terminal composed of a NAND gate of IC ₄ . The output terminal of the inverter is connected to one input terminal of the other NAND gate of IC ₄ , the other input terminal of the NAND gate is connected to the 1Q terminal of IC ₃ , and the output terminal is connected to the driving circuit to drive the 360° light bulb on the sinusoidal curve. 5. A rotary vector demonstrator according to claim 1, characterized in that when the automatic/manual selection button is in the "manual" position, the basic RS flip-flop composed of IC ₂ generates a single pulse, and the single pulse controls the light of the mobile. 6. A rotating vector demonstration instrument according to claim 1, wherein the power supply of the electronic controller is +5V power supply for the electronic controller and AC power supply for the 6V small light bulb.

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