Question

Differential Equations

Question 3 : A buoy bobs up and down in the water following the formula

h(t)=5 \sqrt{3} \sin (2 t)+5 \cos (2 t)

where h is the height above average sea level and t is the time in hours.

(a) What is the period of h?

(b) Show that the buoy reaches a minimum height when t = (2n)/3 and a maximum height when t = (7n)/6.

(c) Find the maximum height of the buoy, that is, the amplitude of h.