If an object suspended from a spring is displaced vertically
from its equilibrium position by a small amount and re-
leased, and if the air resistance and the mass of the spring
are ignored, then the resulting oscillation of the object is
called simple harmonic motion. Under appropriate condi-
tions the displacement y from equilibrium in terms of time
t is given by $y=A\cos \omega t$ where A is the initial displacement at time t = 0, and ω is
a constant that depends on the mass of the object and the
stiffness of the spring (see the accompanying figure). The
constant |A| is called the amplitude of the motion and ω the
angular frequency..... The period T is the time required to make one complete
oscillation. Show that T = 2π/ω.
If I take amplitude equal to $2\pi$ than, I found an equation which is nearly related to period. But, I noticed there's a $\cos$. I don't know how to remove it. How to solve it? I would request for hint.