1. Chapter 11
Vibrations and Waves

2. Spring-mass system

3. Hooke’s Law Felastic = -k x F = elastic spring force (Newtons)
K = spring constant (Newtons/meter)
X = length stretched or compressed from equilibrium

4. Simple Harmonic Motion
Repetitive or oscillating motion about an equilibrium as a result of a restoring force that is proportional to displacement

5. Simple Harmonic Motion Continued
Occurs when restoring force is proportional to displacement.
The maximum displacement from equilibrium is called the amplitude.
The frequency and period depend on the setup, and are independent of the amplitude.

6. Frequency and Period
Frequency: The number of cycles or oscillations per unit time
Measured in Hertz (Hz)
1 Hz = 1 cycle per second
Period: The time for one cycle
f = 1/T
T = 1/f

7. Springs in Oscillation
The period of a spring-mass system in oscillation can be described by…

8. Example
A spring is stretched downward 5.0 cm vertically from is relaxed position when a 500 gram mass is attached.
What is the value of its spring constant?
What would its period and frequency of oscillation be if set into simple harmonic motion?

9. Example
A 350 g mass is attached to a spring with 112 N/m spring constant.
Find the distance the spring stretches.
If the 350 g mass is taken off, how much mass should be placed on there so that it oscillates with a frequency of 1.6 Hz?

10. Pendula

11. Example
How long must a pendulum clock be made so that it keeps a time period of 2.00 seconds in a location where the acceleration due to gravity is m/s2?

12. Example
On the moon, a m long pendulum is observed to oscillate 9.87 cycles in one minute. What is the acceleration due to gravity at that location on the moon?