An object attached to a coiled spring is pulled down a dista

An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up. a = 16; T = 6 seconds a .d = -16 sin (1 /3pit) b.d = -6 cos (1 /8 pit) c.d = -16cos (1 /3pit) d.d = -16 cos (1 /6pit)

Solution

The motion is simple harmonic. Starting position is 16m

S(0)=-16

time period=6s therefore, w=2*pi/6, w=pi/3

As it moves up to satisfy the above conditions the harmonic function must be cosine

S(t)=-16*cos(1/3*pi*t)