Precalculus Mathematics II
7.5 Simple Harmonic Motion Notes
Provide a generalization to each of the key terms listed in this section.
Simple Harmonic Motion
What is the simple harmonic motion?
The simple harmonic motion is a kind of occasional or oscillatory movement that is under a
hindering power relative to the measure of relocation from a balanced or equilibrium position.
Simple Harmonic Motion Formula
Sine Wave Equation
y (t) = A sin 2▯ (t + T)
= A sin T (t) + 2▯
= A sin▯2▯(t)▯
= y (t + T)
y = A sin(!t)
▯ q ▯
= A sin k (t)
v = A! cos(!t)
a = ▯! A sin(!t)
= ▯! y
Total Energy Equation
E = E (K + P)
= KE + PE
1 Simple Harmonic Motion Example
You are given a 9-kg particle that is moving as the following function of time where the distance
is measured in meters while the time’s measured in seconds:
x = 5cos 1:5t +2
What are the motion’s amplitude, angular frequency, and frequency? What would be the velocity
and acceleration formulas of the given particle?
x = A cos(!t + 0