Problem 11: Find the amplitude, frequency and time period of an object oscillating at the end of a spring, if the equilibrium for its position at any instant t is given by x=0.25 cos〖π/2 t〗.
Find the displacement of the object after 2.0 seconds.

Solution

The given equation of the SHM of this particular object is that at any instant of time, t, and distance x from the mean position is given by

If x_{0} is the maximum distance from the mean position (also called amplitude), then the general equation of simple harmonic motion is that the instantaneous distance x from the mean position at any time t is

Compare the given equation of SHM (equation 1) with the general equation of SHM (equation 2),

Therefore,

Amplitude: Amplitude of the oscillating body = 0.25 m

Frequency: We know that

Put the values,

Time period: Since T = 1/f, therefore,

Frequency after 2 seconds:

Now put these values in equation (2) for t = 2 seconds and solve for x.

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