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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)

angular frequency equation for simple pendulum

period equation for simple pendulum

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.


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