1. Simple Harmonic Motion
AP Physics

2. What is periodic motion?
Examples:
Mass on a spring
Pendulum
What do they both have in common?

3. Equilibrium and SHM At equilibrium, net force is zero.
The acceleration is also zero at equilibrium.
Where does this happen for:
A pendulum?
A mass on a spring?
The graph on the right?

4. SHM is like Waves
Crest
Equilibrium Line
The amplitude, A, of a wave is the same as the displacement ,x, of a spring. Both are in meters.
Trough
Period, T, is the time for one revolution or in the case of springs the time for ONE COMPLETE oscillation (One crest and trough). Oscillations could also be called vibrations and cycles.

5. Simple Harmonic Motion
Back and forth motion that is caused by a force that is directly proportional to the displacement. The displacement centers around an equilibrium position. Also known as Periodic Motion.
Pendulum
Mass on a Spring
Uniform Circular Motion
Harmonic Oscillator: object undergoing harmonic motion

6. SHM and Uniform Circular Motion
Springs and Waves behave very similar to objects that move in circles.
The radius of the circle is symbolic of the displacement, x, of a spring or the amplitude, A, of a wave.

7. Simple Pendulum
A simple pendulum consists of a mass, called a bob, suspended by a string or rod of length L.
String or rod is considered massless.
The time to complete one full cycle is a period.
What is the period (T) of the pendulum in the room?

8. Equations: Pendulum and Mass on a Spring
Mass does not effect the motion of the pendulum
What does effect the motion of a pendulum?
‘g’
Length of pendulum
Mass on a Spring
Gravity does not effect the motion of the mass on a spring system
What does effect the motion of the mass on a spring?
Mass
Spring constant
Solve for g and compare to centripetal acceleration

9. Frequency and Period Frequency (f) Period (T)
The number of cycles completed in a period of time.
Total cycles/total time
Units: Hertz (Hz)
Hz = 1/sec
Period (T)
The time to complete one cycle.
Total time/total cycles
Units: seconds

10. Damped Harmonic Motion
SHM
Motion is continuous.
DHM
Motion slows to a stop over time.
The amplitude of motion decreases with time.
Link to Harmonic Motion

11. Example: Energy and SHM
A 200 g mass is attached to a spring that undergoes simple harmonic motion with a frequency of 4 Hz. If the total energy of the system is 2.0 J, find:
The spring constant.
The amplitude of the motion.
126.3 N/m
0.18 m

12. Combinations of Springs
Parallel
Series
Stiffer system
Add to get equivalent
Less stiff system
1/K = 1/K + 1/K
Two springs are combined. The spring constants of each are
100 N/kg and 200 N/kg, respectively. What is the equivalent spring constant
when combined in series? in parallel?

14. Set-up