An object moves in simple harmonic motion with period 6 minutes and amplitude 19m. At time t =0 minutes, its displacement d from rest is −19m, and initially it moves in a positive direction.

Question

Give the equation modeling the displacement d as a function of time t .

Answer 1

The general form for this will be, d(t) = A cos( 2 pi t / T + phi )

We are given,

A = 19 m.

T = 6 min.

( t=0, d(0) ) = (0,-19)

you need to find phi---> d(0) = -19 = 19 cos( 2 pi (0) / 6 + phi )

-1 = cos(phi ) --> phi = pi

d(t) = 19 cos( 2 pi t / 6 + 180 )

you can simplify by noting cos(x+pi) = -cos(x)

d(t) = -19 cos(pi t/3)