Question

A weight is oscillating on the end of a spring. The position of the weight relative to the point of equilibrium is given by y=1/12(cos8t-3sin8t), where y is the displacement (in meters) and t is the time (in seconds). Find the times when the weight is at the point of equilibrium (y=0) for 0<=t<=1.

Answer 1

when y=0
0=1/12 (cos8t-3sin8t)

or
cos8t=3sin8t
tan8t=1/3
8t=arctan 1/3
t= 1/2 arctan 1/3

check my thinking.