1. Ball in a Bowl: F g F N F g F N  F  F Simple Harmonic Motion (SHM) Stable Equilibrium (restoring force, not constant force)

2. 0 m k +x rest position (equation of motion) Hooke’s Law

3. “Guess” a solution: Does it work? Yes, if: … A and C can take any value t x(t) A = amplitude Period = 2  / B B = angular freq. =   22  f So usually written… C = phase lag = 

4. A and  from initial conditions. Example: Mass (m) on spring (k) displaced x = 1 cm at t=0:

5. When a mechanical system is at a point of stable equilibrium, a perturbation will result in a restoring force that drives it back to equilibrium. The resulting equation of motion has the following form: The solution is an oscillating trajectory at frequency  o known as Simple Harmonic Motion.