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A mass that weighs 8 lb stretches a spring 24 in. The system is acted on by an external force of 4 sin 4t lb. If the mass is pulled down 6 in. and then released, determine the position of the mass at any time. Determine the first four times at which the velocity of the mass is zero

Sagot :

Numenius

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]

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