An equation that describes the displacement of an object moving in simple harmonic motion is x(t) = (1.20 m) sin[(2.40 rad/s) t]. What is the maximum velocity of the object?
A) 5.32 m/s
B) 4.82 m/s
C) 3.68 m/s
D) 2.88 m/s
E) 2.03 m/s

Question

Quizplus · Accepted Answer

The maximum velocity of an object in simple harmonic motion occurs when the displacement is zero, which happens at the equilibrium points. Therefore, we need to find the first derivative of the displacement equation and evaluate it at t = 0.

x(t) = (1.20 m) sin[(2.40 rad/s) t]
v(t) = (1.20 m)(2.40 rad/s) cos[(2.40 rad/s) t]

At t=0, cos(0) = 1, so
v(0) = (1.20 m)(2.40 rad/s)(1) = 2.88 m/s

Therefore, the maximum velocity of the object is 2.88 m/s, which corresponds to choice D.

An Equation That Describes the Displacement of an Object Moving