Question
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?
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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