Chapter 15: Oscillations

PHYS2710 - Modern Physics

Relationship Between Frequency and Period

f=\frac{1}{T}

Position in SHM with φ = 0.00

x\left(t\right)=A\cos\left(\omega t\right)

General Position in SHM

x\left(t\right)=A\cos\left(\omega t+\varphi\right)

General Velocity in SHM

v\left(t\right)=-A\omega\sin\left(\omega t+\varphi\right)

General Acceleration in SHM

a\left(t\right)=-A\omega^2\cos\left(\omega t+\varphi\right)

Maximum Displacement (Amplitude) of SHM

x_{\max}=A

Maximum velocity of SHM

\left|v_{\max}\right|=A\omega

Maximum Acceleration of SHM

\left|a_{mac}\right|=A\omega^2

Angular Frequency of a Mass-Spring System in SHM

\omega=\sqrt{\frac{k_{s}}{m}}

Period of a Mass-Spring System in SHM

T=2\pi\sqrt{\frac{m}{k_{s}}}

Frequency of a Mass-Spring System in SHM

f=\frac{1}{2\pi}\sqrt{\frac{k_{s}}{m}}

Energy in a Mass-Spring System in SHM

E_{total}=\frac12k_{s}x^2+\frac12mv^2=\frac12k_{s}A^2

The Velocity of the Mass in a Spring-Mass System in SHM

v=\pm\sqrt{\frac{k_{s}}{m}\left(A^2-x^2\right)}

The x-Component of the Radius of a Rotating Disk

x\left(t\right)=A\cos\left(\omega t+\varphi\right)

The x-Component of the Velocity of the Edge of a Rotating Disk

v\left(t\right)=-v_{\max}\sin\left(\omega t+\varphi\right)

The x-Component of the Acceleration of the Edge of a Rotating Disk

a\left(t\right)=-a_{\max}\cos\left(\omega t+\varphi\right)

Force Equation for a Simple Pendulum

\dfrac{d^2\theta}{dt^2}=-\frac{g}{L}\theta

Angular Frequency for a Simple Pendulum

\omega=\sqrt{\frac{g}{L}}

Period of a Simple Pendulum

T=2\pi\sqrt{\frac{L}{g}}

Newton’s Second Law for Harmonic Motion

m\dfrac{d^2x}{dt^2}+b\dfrac{dx}{dt}+kx=0