SHM

1
SHM Energy

• ET 1/2kA2
• Remember Hookes Law Fkx
• Conservation of energy
• ET KE U
• ET ½kA2 1/2mv2 1/2kx2
• Note with SHM, energy oscillates between KE and
  PE
• At equilibrium position, all KE
• At A or A, all PE

2
SHM applications

• Vertical SHM
• Still restoring force with magnitude kx
• only change equilibrium position
• Angular SHM
• Replace linear parameters with angular
  equivalents
• Restoring torque proportional to angular
  displacement

3
Simple Pendulum

• Idealized model
• Forces gravity and tension
• Fnet mgsin?
• Approxmations if angle small
• Fnet mg?
• Direction of net force roughly horizontal
• Put it all together kmg/L and ? (g/L)1/2
• Frequency independent of mass!