1. Simple Harmonic Motion

2. Ideal Springs F Applied =kx k = spring constant
x = displacement of the spring
+x  pulled displacement
-x  compressed displacement

3. Hooke’s Law F = -kx Describes the restoring force of an ideal spring
Negative sign indicates that this force always goes in the opposite direction of displacement

4. Hooke’s Law
This type of restoring force will create a back and forth or up and down type of motion
This type of friction-free motion is designated simple harmonic motion
The maximum excursion from equilibrium is the amplitude  A

5. Period
Mass-Spring Complex
T = 2π√(m/k)
Pendulum
T = 2π√(L/g)

6. The Reference Circle Simply  a ball moving in uniform circular motion
The shadow cast by the ball on a film creates the same type of sinusoidal pattern
It makes another model of simple harmonic motion

7. Displacement x = A cos q = A cos wt w = 2p/ T f = 1 / T
w = 2pf ( w is often called angular frequency)
X = A cos 2πft

8. Energy & Simple Harmonic Motion
Welastic = ½ kxo2 – ½ kxf2
Us = ½ kx2
ETotal = ½ mv2 + ½ Iw2 + mgh + ½ kx2