Vibration expression: displacement y=y (time t), independent variable is time t.

Wave expression: displacement y=y (position x, time t), independent variables: position x, time t.

Extended data:

(1) mechanical vibration.

The reciprocating motion of an object (particle) on both sides of a central position is called mechanical vibration. An object can move back and forth around an equilibrium position, and it must be subjected to the force that enables it to return to the equilibrium position, that is, the restoring force.

Restoring force is a force named after effect, which can be a force or a component of a force, or a resultant force of several forces. ? The necessary conditions for vibration are: a. The object will be subjected to restoring force after leaving the equilibrium position. B, the resistance is small enough. ?

(2) Simple harmonic vibration.

1. Definition: The vibration of an object under the action of restoring force which is proportional to the displacement and always points to the equilibrium position is called simple harmonic vibration. Simple harmonic vibration is the simplest and most basic vibration.

When studying the position of a harmonic object, a coordinate system with the center position (equilibrium position) as the origin is often established, and the displacement of the object is defined as the displacement of the object from the origin of the coordinate.

Therefore, simple harmonic vibration can also be said to be the vibration of an object under the action of a restoring force that is proportional to and opposite to the displacement, that is, f =-kx, where the "-"sign indicates that the direction of the force is opposite to the direction of the displacement.

2. The condition of simple harmonic vibration: the object must be acted by a restoring force, the magnitude of which is proportional to the displacement from the equilibrium position, and the direction is opposite to the displacement direction. ?

3. Simple harmonic vibration is a kind of mechanical motion, which is applicable to the concepts and laws related to mechanical motion. The characteristic of simple harmonic vibration is that it is a periodic motion, and its displacement, restoring force, speed, acceleration, kinetic energy and potential energy (gravitational potential energy and elastic potential energy) all change periodically with time. ?

(3) Describe the physical quantity of vibration. Simple harmonic vibration is a periodic motion, and the following physical quantities are often introduced to describe the overall vibration of the system. ?

1. Amplitude: Amplitude is the maximum distance between the vibrating object and the equilibrium position, which is usually represented by the letter "a". It is a scalar positive value. The amplitude is a physical quantity representing the vibration intensity, and the amplitude represents the total mechanical energy of the vibration system. In the process of simple harmonic vibration, kinetic energy and potential energy are transformed into each other, and total mechanical energy is conserved.

2. Period and frequency. The period is the time that the vibrator completes a complete vibration, and the frequency is the number of times that the vibrator completes a complete vibration in one second. The relationship between the period t of vibration and the frequency f is reciprocal, that is, t =1/f.

The period and frequency of vibration are both physical quantities describing the vibration speed. The period and frequency of simple harmonic vibration are determined by the nature of the vibrating object itself and have nothing to do with the amplitude, so it is also called natural period and natural frequency.

(4) Simple pendulum:

A simple pendulum with a swing angle less than 5 is a typical simple harmonic vibration. ? One end of the thin wire is fixed at the suspension point, and the other end is tied with a small ball, ignoring the expansion and quality of the wire. A device in which the diameter of the ball is much smaller than the length of the suspension wire is called a simple pendulum.

The condition of simple harmonic vibration of a simple pendulum is that the maximum swing angle is less than 5, and the restoring force f of the simple pendulum is the component of gravity in the tangential direction of the arc. The periodic formula of a simple pendulum is T=.

According to the formula, the natural period of simple harmonic vibration of a simple pendulum has nothing to do with the amplitude and mass of the pendulum ball, but only with L and G, where L is the pendulum length and the distance from the suspension point to the center of the pendulum ball. G is the gravitational acceleration of the position of the simple pendulum. In a system with acceleration (such as a simple pendulum suspended in an elevator), its G should be the equivalent acceleration. ?

(5) Vibration image. ?

The simple harmonic vibration image is a function image of the vibration displacement of the oscillator changing with time. In the established coordinate system, the horizontal axis represents time and the vertical axis represents displacement. The image is a sine or cosine function image, which directly reflects the periodic variation law of simple harmonic dynamic displacement at any time.

It is necessary to relate the vibration process of the particle with the vibration image, from which we can get the changes of displacement, velocity, acceleration and restoring force of the vibrator at different times or positions.

(6) Damping vibration, forced vibration and * * * vibration. Simple harmonic vibration is an idealized vibration. When external energy is given to the system, if the vibrator is pulled away from the equilibrium position and released, it will keep vibrating, and the amplitude of the vibrator is constant in the image of simple harmonic vibration.

It shows that the mechanical energy of the system is constant, there is always resistance in actual vibration, and the vibration energy is always dissipated, so the mechanical energy of the vibration system is always decreasing, and its amplitude is gradually decreasing until it stops.

Vibration with reduced amplitude is called damping vibration. Damped vibration is called undamped vibration. Although its amplitude is getting smaller and smaller, its vibration period and amplitude remain unchanged.

If a vibrating object vibrates under the action of periodic external force, it is forced to vibrate. When the forced vibration reaches stability, its vibration period and frequency are equal to those of the driving force, regardless of the natural period or frequency of the vibrating object.

The amplitude of the forced vibration of an object is related to the period (frequency) of the actuating force and the natural period (frequency) of the object. The smaller the difference between them, the greater the amplitude of the forced vibration of the object. When the period or frequency of the actuating force is equal to the natural period or frequency of the object, the amplitude of the forced vibration is the largest, which is called * * * vibration. ?

References:

Baidu Encyclopedia-Vibration of Objects

References:

Baidu encyclopedia-fluctuation