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Equations of Simple Harmonic Motion

Mass on a Spring

Objective 1: To understand the derivation of the period and frequency equation for a mass on a spring

Objective 2: To be able to state the dependent variables for the period and frequency of a mass on a spring

1. Newton's Second Law combined with Hooke's Law

F = ma = kr

2. Solve for acceleration a

a = kr/m

3. Equate to the corresponding acceleration in circular motion

a = kr/m = w^2r

4. Solve for w, this gives the angular frequency equation

w = Square root (k/m)


Angular Frequency Equation of SHM for a mass on a spring:

Equation for angular frequency omega eqauls seaure rot of k/m


Period Equation of SHM for a mass on a spring:

equation for period euqals 2 pi square root m/k


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