The displacement of an object oscillating on a spring is given by x(t) = x_mcos( $ \omega $t + $\phi$). If the object is initially displaced in the negative x direction and given a negative initial velocity, then the phase constant $\phi$ 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 ($\phi$ is exactly 0, $\pi$/2, $\pi$, or 3 $\pi$/2 radians)

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Quizplus · Accepted Answer

Given that the object is initially displaced in the negative x direction and given a negative initial velocity, we can conclude that the phase constant must be between F1F1F1S1F1F1F10/2 and F1F1F1S1F1F1F10 radians. This is because the cosine function in the displacement equation has a maximum value of 1 when the phase constant is 0, and the object starts with a negative displacement and negative velocity, so the cosine function must start at its minimum value of -1. Therefore, the initial displacement equation is x(t) = -x_mcos(F1F1F1S1F1F1F10t + F1F1F1S1F1F1F10), which falls under the interval of F1F1F1S1F1F1F10/2 and F1F1F1S1F1F1F10 radians.

The Displacement of an Object Oscillating on a Spring Is ω \omega ω

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