Champions League

List of contents of this article:

• 1,Champions League What is the single pendulum principle
• 2, In different motion systems, the force of the single pendulum
• 3, High school physics single pendulum problem

What isSingle pendulum principle

Single pendulum is a device that can produce reciprocating swing. One end of a thin rod or a thin soft rope that cannot be stretched hangs at a certain point in the gravity field, and the other end solidifies a heavy ball to form a single pendulum. If the ball is limited to the swing in the lead straight plane, it is a plane single pendulum. If the ball swing is not limited to the lead straight plane, it is a spherical single pendulum.

Single pendulum motion refers to the movement of a mass point along a swing trajectory (i.e. a straight line) in a gravitational field. The point is suspended by a line that is absolutely flexible, the length is constant and the mass is negligible, and it moves periodically in the plumb plane under the action of gravity.

Hang a point of mass with an absolutely flexible, constant length and negligible mass, and make a periodic movement in the plumb plane under the action of gravity, which becomes a single pendulum.When a single pendulum vibrates under the condition that the pendulum angle is less than 5° (now generally considered to be less than 10°), it can be approximately regarded as a simple harmonic 1 movement.

The single pendulum experiment was originally done by Galileo, that is, when the swing angle of the swing ball is very small (less than 5°), the pendulum will do periodic swings. The swing period is directly proportional to the pendulum length. The longer the pendulum is, the longer the pendulum period is.

In different motion systems, the force on the single pendulum

1. The force analysis of the single pendulum movement is as shown in the figure, a point is hung with an absolutely flexible line of constant length and negligible mass, and under the action of gravity in the plumb plane Periodic movement becomes a single pendulum.

2. In a single pendulum (or simple harmonic vibration), the pendulum is subjected to two main external forces: gravity and tension.

3. At this time, the single pendulum ball (object) is affected by two forces, namely its own weight and the pulling force of the rope. And on the same straight line, the combined force of the two provides the centripetal force of circular motion. The method of judging whether the force of an object is balanced: look at whether the state of motion of the object changes, because force is the reason for changing the state of motion of the object.

High school physics single pendulum problem

1, [Analysis] 1) The first release is the long pendulum, so there is nT1=nT2+Δt, and the solution is n=25, so the release time of the short pendulum is t=n T2=085s. At this time, the two At the same time, the swing passes the balance position to the left. 2) Increase the pendulum length without changing the pendulum length difference. The smaller the △T, the smaller the time difference that can be measured.

2. Answer: The amplitude and mechanical energy of the single pendulum change. The periodic formula T=2π(L/g)^1/2 of the single pendulum increases the mass of the pendulum ball, and the single pendulum period remains unchanged.

3. The high school physics single pendulum period formula is derived to establish the Lagrange equation, linear approximation solution, period formula, etc.Establish the Lagrange equation. Considering the motion of a single pendulum, we can establish its Lagrange equation. The Lagrange equation describes the motion of the system, which is expressed by the difference between the kinetic energy T and the potential energy U.

4. The first case is two identical single pendulums. Therefore, the inherent cycle is the same. One drives the other, and the two single swings are the same. There is no external force applied by the outside world, and the kinetic energy of the two balls is the same. Ideally, it will always swing consistently.