1. Energy And SHM

2. Energy of Spring Spring has elastic potential energy PE = ½ kx 2 If assuming no friction, the total energy at any point is the sum of its KE and PE E = ½ mv 2 + ½ kx 2

3. At Extreme Stops moving before starts back, so all energy is PE and x is max extension (A) E = ½ k A 2 At equilibrium, all energy is KE and v o is the max velocity E = ½ m v o 2

4. Algebraic Manipulation

5. Example If a spring is stretched to 2A what happens to a) the energy of the system? B) maximum velocity? C) maximum acceleration?

6. Example A spring stretches.150m when a.300kg mass is hung from it. The spring is stretched and additional.100m from its equilibrium point then released. Determine a) k b) the amplitude c) the max velocity d) the velocity when.050 m from equilibrium e) the max acceleration

7. Example For the previous example find a) the total energy b) the kinetic and potential energies at half the amplitude