Acceleration in Simple Harmonic Motion
x(t) = A cos (wt+ ϕ)
dx/dt = V = -Aw sin (wt+ ϕ)
a = dV/dt = d/dt .-Aw sin (wt+ ϕ)
a = -Aw d/dt . (sin(wt+ ϕ))
a = - Aw cos(wt+ ϕ).w
= -w2 A cos(wt+ ϕ)
a = -w2 x
case 1:
x=0
a=0
In a mean position accleration is minimum
case 2:
x=A
a = -w2 A
In a extreme position accleration is in a maximum acceleration.
x(t) = A cos (wt+ ϕ)
dx/dt = V = -Aw sin (wt+ ϕ)
a = dV/dt = d/dt .-Aw sin (wt+ ϕ)
a = -Aw d/dt . (sin(wt+ ϕ))
a = - Aw cos(wt+ ϕ).w
= -w2 A cos(wt+ ϕ)
a = -w2 x
case 1:
x=0
a=0
In a mean position accleration is minimum
case 2:
x=A
a = -w2 A
In a extreme position accleration is in a maximum acceleration.
