1. Measuring Harmonic Motion

2. Amplitude
Maximum displacement from the equilibrium position

3. Period Period is represented by T
T= is the time it takes for a complete cycle of motion measured in seconds
During T , the displacement is zero

4. Frequency Frequency is represented by f
f= is the number of complete cycles through a unit of time
SI units of s-1 (Hertz)

5. Frequency and Period Frequency and period are inversely proportional
F= 1/T and T= 1/F
F is # of cycles/per unit time
T is time /cycle

6. Period of a Simple Pendulum
Depends on string length and free fall acceleration
Ex. #1 - 2 pendulums with different masses, have the same period
Ex. #2 - 2 pendulums have different amplitudes, have the same period

7. Period of a Simple Pendulum
T = 2 ∏ √ (L/g)
Period = 2 ∏ X √ (length divided by 9.81)

8. Period of a Simple Pendulum
Why does the length of the string affect the period?
The shorter the pendulum, the smaller the arc to travel through

9. Period of a Simple Pendulum
Why doesn’t the mass and amplitude affect the period?
Heavier mass has a greater restoring force and larger force to achieve the same acceleration
Free fall is the same, regardless of the mass

10. Period of a Mass-Spring System
Restoring force is determined by the displacement
Magnitude of the mass, does not affect the restoring force
Therefore, mass increased both force on the spring and the spring’s inertia

11. Period of a Mass-Spring System
Heavy masses have smaller accelerations, than light masses
Heavy masses will take more time to complete one cycle of motion
Heavy masses = greater period

12. Period of a Mass-Spring System
Greater the spring constant = greater force and acceleration
Period will decrease

13. Period of a Mass-Spring System
T = 2 ∏ √ (m/k)
Period = 2 ∏ √ (mass divided by spring constant)