Physics 101- Introduction to Mechanics
April 29- SHO & Pendulums

 

 

 

 
 

 

  Here, we rely on the fact that sinq =q

How true is this approximation?  Compare the two sides for 5°, 10°, 20°
 

Recall the equation of motion for a mass on an ideal spring:

Notice how the pendulum's equation of motion looks the same as the spring's?  This means we already know the solution.
 
 

It is easy to see how this derivation can be extended to any swinging shape. We simply need the correct I and the correct torque.
 
 
 
 
 

  • How long should a simple pendulum be to make its period 2 seconds?

 
 
  • Now you place this pendulum in an elevator.  Upon doing this you notice that by your digital timer, the period of the pendulum is now 2.1 seconds.  Describe the motion of the elevator.

 
 
 
 
 

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Jeff Phillips
phillips@lmu.edu
Loyola Marymount University
Spring 2002