1. 11-2 : Measuring SHM

2. Amplitude, Period, and Frequency
Amplitude: the maximum displacement from the equilibrium position.
Amplitude is given in radians or meters.
Period: the time it takes to execute a complete a full cycle of motion.
Period(T) is given in seconds.

3. Frequency and period are inversely related
Given a certain unit of time, the frequency is given by the number of complete cycles that occur in that amount of time.
Frequency symbol = f unit = Hertz (Hz).
Frequency and period are inversely related
f = T-1

4. Period of a Simple Pendulum
Depends only on the string length and the acceleration due to gravity.
T= Period
L=Length of string
g=Free-fall acceleration
With different masses, the restoring force changes to accommodate to the new mass, and thus there is no change in period.
The restoring force also increases with a greater amplitude, but then there a different distance, so the changes cancel out and there is no change in period.)

5. Period of a Mass-Spring System
With a mass-spring system, mass does have an effect on the period.
as mass increases, the period also increases.
The greater the spring constant(k), then the higher the force that is required to stretch or compress the spring, thus a higher acceleration, which would bring a smaller period.
Therefore, the higher the spring constant, the smaller the period.
T=Period
m=Mass
k=Spring Constant

6. Sample Problem
You desire to find the height of a small-model skyscraper so you attach a pendulum to the ceiling and it takes 15 seconds for the pendulum to return to the equilibrium location. How tall is the tower?

7. Sample Problem (solved)
t= 15 seconds g=9.81 m/s² L=?

8. Sample 2
A pendulum makes 11 oscillations in 12 s. Find its period and frequency. Also find its period on Jupiter if the accel. due to gravity is 24.8 m/s2.
Given:
t = 12 s
# of cycles = 11

9. f = # of cycles/ time = 11/12s = 0.92 Hz
T = f-1 = 1/0.92 Hz = 1.09 s
On earth,

10. On Jupiter: