An object at the end of a vertical spring is straightened 3 cm beyond its rest p

Question

An object at the end of a vertical spring is straightened 3 cm beyond its rest position and released at time t = 0. (Note the downward position in the figure.) Its position at time t is: s = f(t) = 3 cos(t)

If you could help fill in the blanks based on this information, and explain it that would be great.

The object oscillates from the lowest point (s = 3 cm) to the highest point (s = -3 cm). The period of the oscillation is _____ the period of cos(t). The speed is |v| = |-3sin(t)|,  which is greatest when |sin(t)| =______. that is, when cos(t) = 0. So the object moves fastest as it passes through its equilibrium position (s = 0). Its speed is 0 when sin(t) = _______ , that is, at the high and low points.

The acceleration a = ________ = 0 when s = 0. It has greatest magnitude at the high and low points. See the graphs to the left.

Explanation / Answer

An object at the end of a vertical spring is straightened 3 cm beyond its rest position and released at time t = 0. (Note the downward position in the figure.) Its position at time t is: s = f(t) = 3 cos(t)

If you could help fill in the blanks based on this information, and explain it that would be great.

The object oscillates from the lowest point (s = 3 cm) to the highest point (s = -3 cm). The period of the oscillation is 2p, the period of cos(t). The speed is |v| = |-3sin(t)|,  which is greatest when |sin(t)| =1. that is, when cos(t) = 0. So the object moves fastest as it passes through its equilibrium position (s = 0). Its speed is 0 when sin(t) = 0 , that is, at the high and low points.

The acceleration a = -3cost = 0 when s = 0. It has greatest magnitude at the high and low points. See the graphs to the left.

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