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. Assume that the motion is simple harmonic with period T. Write an equation that relates the distance d of the object from its rest position after t seconds.

a = 17
T = 3pi seconds

Solution

An object that moves on a coordinate axis so that its distance,d, from the origin at time,t, with angular

where a and speed, , is given by either d = acos(wt) or d = asin(wt) are constants, moves with simple harmonic motion.

w = 2pi/T = 2pi/3pi = 2/3 ; a=17

d = 17cos(2t/3)