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The X component of the velocity of an object vibrating along the X-axis obeys the equation...

The X component of the velocity of an object vibrating along the X-axis obeys the equation Vx(t) = (0.444 m/s) sin[(25.4 rad/s)t + 0.223].

A. What is the amplitude of the motion of this object?
B. What is the maximum acceleration of the vibration object?
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Homework Answers

Answer #1

The motion given in the equation is sinusoidal, so if we compare it to x = X sin( wt + phi)

Here, X is the amplitude of the motion. ( Amplitude is the maximum value of the quantity being measured in the equation)

Therefore on comparing, we get the amplitude of the motion of the object as 0.444 m/s

b)

Acceleration,   ; v = V* sin(wt +phi)

therefore, a = Vw* cos ( wt+phi) ====> Maximum acceleration is the amplitude of 'a'

Therefore Maximum acceleration is V*w = 11.2776 m/s2

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