A weight attached to a spring is pulled down 7 inches below

A weight attached to a spring is pulled down 7 inches below the equilibrium position. Assuming that the period of the system is 1/9 second, determine a trigonometric model that gives the position of the weigh at time t second.

Solution

comparing with y =a cos(bt)

initial position is 7 inches below the equilibrium position =>t =0,y =-7

-7= a cos(0)

a =-7

given period =1/9

2pi/b =1/9

=>b =9*2pi

=>b =18pi

y =-7 cos(18pi t) is equation of motion