1. Chapter 11: Harmonic Motion
Elastic Potential Energy
energy stored in a stretched/compressed spring
Force: Hooke’s Law F = kx
F = 0
F = k x/2
F = k x x
unstretched
half stretched
stretched

2. A horizontal spring had a force constant of 90 N/m. A mass of 1
A horizontal spring had a force constant of 90 N/m. A mass of 1.5 kg is attached free end. The spring is then compressed by 50 cm, and then released. What is the speed of the mass when it returns to the equilibrium position?

3. Simple Harmonic Motion: oscillations
Period T = time for one complete oscillation
frequency f = number of oscillations per time
usually number per second (1 cycle/sec = 1 Hertz = 1Hz)
f = 1/T
for a restoring force (equilibrium) + inertia
Fr = kx plus F = ma

4. Position, speed and acceleration in simple harmonic motionx
maximum speed at x = 0
Amplitude A = xmax
v = 0 when x = xmax
x = A cos 2ft = A cos t t

5. Example: An object undergoes SHM with a frequency of 20 Hz and a maximum speed of 2.5 m/s. What is the amplitude of the motion? What is the object’s displacement when its speed is 1.5 m/s?

6. mass m on a string of length L
The Simple Pendulum
mass m on a string of length L x s mg T
Fnet L
Example: How long should a pendulum be in order to have a period of 1.0 s?