In an oscillatory system we have already seen that the position function can be

Question

In an oscillatory system we have already seen that the position function can be represented by the equation x(t)=Acos(t+) This problem is designed to help you to understand to identify the phase shift for different conditions. In each situation, we will consider a horizontal oscillation with a single mass attached to a single spring. You may assume that both air resistance and friction are negligible for this oscillation. The center of the oscillation is the equilbrium position and is chosen to be zero position. Positive positions are to the right of this location and negative positions are to the left. Part D - As we have seen, there are some standard types of situations where the phase shift is used to change between sine or cosine graphs, but what happens if the phase shift is a bit more random? Consider a case where the oscillator is started randomly such that the amplitude is 0.250 meters, the angular frequency is 2.50 radians / second, and the initial oscillator position is -0.117 meters (with the mass moving in the positive direction). What phase shift would be required? Give your answer in radians within the range - 2+2 .

Explanation / Answer

X = A*sin(Wt+phi)

at time t = 0

initial position X = -0.117 m

angular frequency w = 2.5 rad/s

amplitude A = 0.25 m

-0.117 = 0.25*sin(0+phi)

phi = 3.63 rad <<<----answer

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