Simple Harmonic Motion (SHM)

Simple Harmonic Motion – Vibration about an equilibrium position in which a restoring force is proportional to displacement Examples?

Mass Spring System F max a max Equilibrium v max F max a max

Spring Mass Systems K = spring constant X = displacement from relaxed position F = restoring force *If a spring is stretched or compressed, it oscillates in SHM when it is released.

Simple Pendulum F max a max Equilibrium v max F max a max

Energy Relationships in SHM At equilibrium – KE is at a maximum At maximum displacement – PE is at a maximum PE transferred to KE then transferred back to PE Total energy is conserved

Simple Harmonic Motion Maximum Displacement Equilibrium Maximum Displacement Equilibrium Maximum Displacement

Vocabulary Amplitude – Period – Frequency

Equations Period of a simple pendulum in SHM T = 2π√(L/a g ) T = period (s) L = length of pendulum (m) a g = gravity (m/s 2 ) Period of a mass –spring system in SHM T = 2π√(m/k) T = period (s) m = mass (kg) k = spring constant (N/m)