Simple Harmonic Motion

Displacement of Simple Harmonic Motion: x(t)=A cos(ωt+ϕ)

Angular Frequency: ω=2πf = 2𝜋

𝑇

Velocity of Simple Harmonic Motion: v(t)= -(ωA) sin(ωt+ϕ)

=ωA cos(ωt+ϕ+π/2)

vmax = ωA

Acceleration of Simple Harmonic Motion: a(t)= -ω2 (A cos(ωt+ϕ))

=-ω2 x(t)

Restoring Force : F(t)=ma(t)=-mω2 x(t)

Mass-Spring System : Fspring =-kx

Fnet =Fspring=-kx =max

ω2 =𝑘

𝑚

ω =√𝑘

𝑚

T= 2π√𝑘

𝑚

f =1

2π√𝑘

𝑚