A Simple Pendulum and Friction problem

In summary, to calculate the work done by friction on a simple pendulum after one period, one must use the equation ((beta)^2)'= (2g/l)(cosbeta - costheta) where theta is the maximum angle of motion. This is the angle at which the derivative of beta equals 0 and l is the length of the pendulum string. To determine the path of the pendulum, information such as initial position and length of the wire must be given.
  • #1
Ed Quanta
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Im supposed to calculate the work done by the frictional force on a simple pendulum after one period. I have to use the following equation to do this calculation.

((beta)^2)'= (2g/l)(cosbeta - costheta) where thetha is the the maximum angle of the motion.
In other words theta is the angle at which the derivative of beta=0. l is the length of the pendulum string.

How do I use this equation to determine the path taken by the pendulum so I know what I am integrating the force of friction over?

By the way, I am given information regarding the initial position of the ball above the floor, the length of the pendulum wire, and the ceiling height.
 
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  • #2
Nevermind the help, I figured it out. It was an easy question. Sorry for wasting internet space.
 

1. What is a simple pendulum?

A simple pendulum is a mass attached to a string or rod and suspended from a fixed point. It is used to study the effects of gravity and to measure time intervals.

2. What is the equation for the period of a simple pendulum?

The equation for the period of a simple pendulum is T = 2π√(L/g), where T is the period (time for one complete swing), L is the length of the string or rod, and g is the acceleration due to gravity.

3. How does friction affect a simple pendulum?

Friction can cause a decrease in the amplitude (height) of the pendulum's swing over time, as it converts the pendulum's kinetic energy into heat energy. Friction may also slightly affect the period of the pendulum, but this effect is usually negligible.

4. What are some examples of friction in a simple pendulum?

Examples of friction in a simple pendulum include air resistance, which can slow down the pendulum's swing, and friction at the pivot point, which can cause the pendulum to stop swinging altogether. Friction in the string or rod can also affect the pendulum's motion.

5. How can friction be minimized in a simple pendulum?

To minimize friction in a simple pendulum, it is important to use a smooth, lightweight string or rod and to make sure that the pivot point is well lubricated. Reducing the amplitude of the pendulum's swing can also help to reduce the effects of friction.

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