Question

The position of a 60 g oscillating mass is given by x(t)=(2.0cm)cos(10t), where t is in seconds. determine the velocity at t=0.40s.

Answer 1

The position of an oscillating mass is given by:

$x(t)=A cos (\omega t)$

where A is the amplitude of the oscillation, $\omega$ the angular frequency and t the time.

The velocity of the oscillating mass can be found by calculating the derivative of the position:

$v(t)=x'(t)=-\omega A sin (\omega t)$

In this problem, A=2.0 cm and $\omega=10 rad/s$, so if we substitute these data and t=0.4 s we can find the velocity at t=0.4 s:

$v(t)=-(10 rad/s)(2.0 cm) sin ((10 rad/s)(0.4 s))=-13.07 cm/s=-0.13 m/s$