1. Energy of Simple Harmonic Motion

2. Work and Springs
When a spring is stretched or compressed, work is done on the spring
When a spring is stretched, the effort (force) varies from 0 to a maximum value. Therefore, we use the average force to calculate the work done in stretching a spring.

3. Work and Springs
If work is done on a spring, then the spring must possess stored energy (a.k.a. elastic potential energy)
As the spring vibrates back and forth, Ep is converting to Ek, back to Ep, back to Ek and so on, and so on

4. Springs and Total Mechanical Energy
At the equilibrium position the spring has:
Maximum kinetic energy
Maximum speed
No potential energy
At maximum displacement the spring has:
Maximum potential energy
No kinetic energy

5. Springs and Total Mechanical Energy
We can see that the kinetic energy at equilibrium is equal to the potential energy at maximum displacement

6. Springs and Total Mechanical Energy
We can use the following equation to find the velocity of an object at any position:

7. Sample Problem
An object vibrates at the end of a vertical spring (k=121 N/m). If the Ep of the object is 2.20J, what is its displacement?

8. Sample Problem
A 0.30 kg mass vibrates at the end of a horizontal spring along a frictionless surface. If the spring constant is 45 N/m, and the maximum displacement of the mass is m, what is the maximum speed of the mass?

9. Homework
Go over handout
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