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Classical Mechanics

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Moderate

Oscillations: Find the Time

CLMECH-LLE4GY

A mass is attached to a vertical spring mounted in the ceiling. The mass is set into motion such that its equation of motion is:

$$x(t)=A\sin(2\,\pi\,f\,t)$$

where $A$ is the amplitude of motion, $f$ is the frequency and $t$ is time. Take $f=60.0\,Hz$.

What is the first time that the position is equal to $x=-0.800\,A$ and the velocity is positive?