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 |

## 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.