The displacement of an object oscillating on a spring is given by x(t)= x_mcos( + ).If the object is initially displaced in the negative x direction and given a negative initial velocity, then the phase constant is between: A)"0 and $\pi$ /2 radians" B)" $\pi$ /2 and $\pi$ radians" C)" $\pi$ and 3 $\pi$/2 radians" D)"3 $\pi$ /2 and 2 $\pi$ radians" E)"none of the above ( is exactly 0, $\pi$ /2, $\pi$ , or 3 $\pi$ /2 radians)"

Question

Quizplus · Accepted Answer

Since the object is initially displaced in the negative x direction and given a negative initial velocity, the displacement x(t) must start at its maximum negative value and be decreasing as time goes on. This means that the cosine function in x(t) is negative at t=0. The only way for the cosine function to be negative at t=0 is if the phase constant F1F1F1S1F1F1F10F1F1F1S1F1F1F10 is between F1F1F1S1F1F1F10/2 and F1F1F1S1F1F1F10 radians. Therefore, the answer is B.

The Displacement of an Object Oscillating on a Spring Is π\piπ

The Displacement of an Object Oscillating on a Spring Is $\pi$