| Dissertation |
| SHM Properties | SHM Applications | SHM Relations | SHM Graphs | Graphical Relations | SHM and Circular Motion | SHM Equations | Simple Pendulum | Simple Pendulum Graph | Simple Pendulum Equations | SHM Assessment |
Equations of SHM for the Simple Pendulum
Objective 1:: To understand the derivation of the period and frequency equation for a simple pendulum.
Objective 2: To be able to state the dependent variables for the period and frequency of a simple pendulum
1. Equate restoring force and Hooke's Law: (Reference: Properties of SHM)
F = mgsin(theta) = kr = ks
2. Solve for k
k = mg sin(theta)/s
3. Substitute s = L(theta) (Reference: Simple Pendulum Illustration)
k = mg sin(theta)/L(theta)
4. Make the small angle approximation that sin(theta) = (theta)
k = mg (theta)/L(theta
5. Simplify
k = mg/L
6. Substitute into f and T equations of SHM (Reference: Equations of SHM)
Important Note: The period, T, and the frequency, f, of a Simple Pendulum depend only on Length, L, and gravity, g. The Period, T, and frequency, f, do not depend on mass.