SIMPLE HARMONIC MOTION

Back & forth & back & forth

Are you getting sleepy?

HARMONIC MOTION – BACK & FORTH OVER THE SAME PATH

X = displacement – distance pulled/stretched from equilibrium

When released – spring exerts a force on the mass towards equilibrium

Vmax @ equilibrium p causes it to overshoot @ max stretch/compression –

V = 0, acceleration & force @ max

REMEMBER HOOKE’S LAW? Felastic = -kx

Pendulums

PENDULUM Disregard mass of string, air resistance,

friction If restoring F proportional to

displacement = harmonic motion Small angles of displacement equal

simple harmonic motion Free body diagrams (miss them?!) to

Resolve into x & y components

Amplitude = max displacement from equilibrium (rad or m)Angle of pendulum, spring

stretched/compressed Period = one full cycle of motion (T) in

secondsTime per cycleDepends on length of the string & free fall

acceleration Frequency = # of cycles through a unit

of time (f) in Hertz

or

L = length of the string g = acceleration due to gravity

String length varies = different arc lengths to travel through = different T

Mass varies = no effect on T (more force to restore equilibrium but more force to start)

Amplitude = affected by g

For springs:

m = mass K = spring constant Mass affects period

< mass = < T