PHYSICS QUESTION on OSCILLATIONS

The position of a mass oscillating on a spring is given by x=(5.0 cm)cos[(2pi(t))/(0.67 s)].


What is the period of this motion?
T=_____s

What is the first time the mass is at the position x=0?
t=_____s




thanks

cos is periodic with a periodicity of 2 pi, the period of the oscillator is 0.67s, since each integral multiple of 0.67s results in the cos returning to the same value

the mass is at x=0 when the argument of the cos (the stuff inside the cos brackets] equals pi/2 since the cos of pi/2 =0

therefore, 2 pi t/0.67 = pi/2

t = 0.67/4 = 0.167s