A mass free to vibrate on a level, frictionless surface at the end of a horizontal spring is pulled 35 cm from its equilibrium position and released. At an instant 0.12 s later, its displacement has decreased to 15 cm, without the mass having passed through equilibrium. Calculate the period. ( 0.67 s).

0.67 s

Explanation:

This is a simple harmonic motion (SHM).

The displacement, , of an SHM is given by

A is the amplitude and is the angular frequency.

We could use a sine function, in which case we will include a phase angle, to indicate that the oscillation began from a non-equilibrium point. We are using the cosine function for this particular case because the oscillation began from an extreme end, which is one-quarter of a single oscillation, when measured from the equilibrium point. One-quarter of an oscillation corresponds to a phase angle of 90° or radian.

From trigonometry, if A and B are complementary.

At ,

So

At ,

The period, , is related to by

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