Question

The position of a 45 g oscillating mass is given by x(t)=(2.0cm)cos(10t), where t is in seconds. determine the velocity at t=0.40s. express your answer in meters per second to two significant figures.

Answer 1

The position of the oscillating mass, in meters, is
$x(t) = (0.02 m) \cos (10 t)$

its velocity is the derivative of the position:
$v(t)=x'(t) = -(0.02 m/s)(10)\sin (10 t) = -(0.20 m/s) \sin (10 t)$
since the derivative of the cosine is -sine.

Therefore, to find the velocity of the oscillating mass at time t=0.40 s, we can substitute this value into the expression of the velocity:
$v(0.40 s)=-(0.20 m/s) \sin (10 \cdot 0.4 s)=-0.15 m/s$