Simple Harmonic Motion

When the displacement of an oscillating object from an equilibrium position varies with time as a cosine (or a sine) function, the periodic motion is called simple harmonic motion.

$x(t)=A\cos (\omega t+\varphi )$

• $A$ is the amplitude → the maximum displacement of the oscillator from its equilibrium position
• $\omega$ is the angular frequency $\omega =2\pi f=\frac{2\pi }{T}$
• $\varphi$ is the phase constant (the “shift”)

Velocity and Acceleration

$v(t)=-\omega A\sin (\omega t+\varphi )$ $a(t)=-{\omega }^{2}x(t)$

Various things go through Simple Harmonic Motion, including:

• Mass-Spring System
• Pendulum System

Misc Facts

In ECE140, we learned that the RMS value of a sin function is: $V_{rms}=\frac{V_m}{\sqrt{2}}$

Related

• Linear Harmonic Oscillator (MATH213 stuff)