Trig function

Question

1.A mass on a spring moving up and down is an example of harmonic motion. If the height of the spring mass system follows the function h(t)=5cos2t , where t is the time in seconds and h is the height from equilibrium in inches. What are all of the exact times than the height is 2.5 inches?

 

Answer 1

2.5 = 5 cos² t

0.5 = cos² t

√2 / 2 = cos t

t = π/4 + 2kπ

t = 7π/4 + 2kπ