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Answer:
[tex]t = \frac{\pi}{8}, \frac{\pi}{4}, \frac{3\pi}{8}, \frac{3 \pi}{4}[/tex]
Explanation:
The equation of force is
F = 4 sin 4 t
Compare with the standard equation
f = A sin wt
where, w is the angular frequency and A is the amplitude.
Now
w = 4 rad/s
Let the time period is T.
the relation for the time period is
[tex]T = \frac{2\pi}{w}\\\\T = \frac{2 \pi}{4}\\\\T = \frac{\pi}{2}[/tex]
the time period is defined as the time taken by the body to complete one oscillation.
So, the velocity is zero at the extreme points where the object is at time, T/4 and its odd T/2, 3T/4, 3T/2, etc.
So, the velocity is zero at time
[tex]t = \frac{\pi}{8}, \frac{\pi}{4}, \frac{3\pi}{8}, \frac{3 \pi}{4}[/tex]