For an object in damped harmonic motion with initial amplitu

For an object in damped harmonic motion with initial amplitude a, period 2/, and damping constant c, find an equation that models the displacement y at time t for the following. (a) y = 0 at time t = 0 (b) y = a at time t = 0

Solution

(a) y = 0 at time t = 0
if the period is 2/ then the frequency = w /2
and the radian frequency = 2 x frequency = w
y = a sin( wt)

(b) y = a at time t = 0
y = a cos (wt)