Question 966917
Given,  y = 8+7cos3t + 7cos6t

when y=8 cm

8=8+7cos3t + 7cos6t

can be rearranged as 

7(cos3t+cos6t)=0

or cos3t+cos6t =0 

2cos(9t/2).cos (3t/2)=0              {cosA + cosB = 2 cos(A+B/2).cos(A-B/2)}

or cos(9t/2).cos (3t/2)=0

This means either cos(9t/2)=0 or cos (3t/2)=0

if cos(9t/2)=0

9t/2= n(pi)/2

t=n(pi)/9

if cos (3t/2)=0

3t/2= n(pi)/2

t=n(pi)/3

The first time when displacement is 8 cm is t=pi/9