The displacement of an object oscillating on a spring is given by x(t)= x_mcos(+ ).If the initial displacement is zero and the initial velocity is in the negative x direction, then the phase constant is: A)"0 radians" B)"$\pi$/2 radians" C)"$\pi$ radians" D)"3$\pi$/2 radians" E)"2$\pi$ radians"

Question

Quizplus · Accepted Answer

Since the initial velocity is in the negative x direction, we know that the object starts by moving towards the equilibrium point with a negative velocity. This means that at time t=0, the object is located at the maximum displacement in the negative direction. Therefore, we can write:

x(0) = -xS1

Plugging this into our equation for x(t), we get:

-xS1 = xS1 U1B1mS1U1B0 cos(F1F1F1S1F1F1F10)

We can simplify this to:

cos(F1F1F1S1F1F1F10) = -1

Which means that the phase constant F1F1F1S1F1F1F10 must be an odd multiple of pi/2. The only answer choice that satisfies this condition is B, F1F1F1S1F1F1F10/2 radians.

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

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