ch 7 simple harmonic motion

Hooke’s law

F = -kx

Hooke’s Law for vertical motion

F = mg - kx

frequency in general

f = 1/T

period in general

T = 1/f = time/rev = time/# of cycles

period for mass spring system

T = 2pi/w = 2pi* sqrt (m/k)

frequency for mass spring system

f = 1/T = w/2pi = 1/2pi* sqrt(k/m)

angular frequency

w = sqrt(k/m)

max velocity

Aw = A*sqrt(k/m)

max acceleration

Aw²

restoring force for pendulum

Fx = mg sin(theta)

x component

period for pendulum

T = 2pi * sqrt(L/g)

frequency for pendulum

T = 1/2pi * sqrt(g/L)

elastic potential energy of spring

U = 1/2kx²

kinetic energy of simple harmonic motion

KE = 1/2mv²

total mechanical energy

ME = KE + U = 1/2mv² + 1/2kx²

total mechanical energy at maximum displacement

ME = KE + U = 0 + 1/2kx² = 1/2kA²

total mechanical energy at equilibrium

ME = KE + U = 1/2mv² + 0 = 1/2mv_max²

total mechanical energy between max displacement and equilibrium

ME = KE + U = 1/2mv² + 1/2kx²