An object attached to a spring is pulled down a distance of 3 inches below the point of equilibrium. it completes one oscillation in 2 seconds. find the equation of the motion, when will it have covered a distance of 9 inches.

Explanation:

The equation of motion in simple harmonic motion is

where Ф is the phase angle to be determined by the initial conditions.

At t = 0, the object is pulled 3 inches, which means A = 3.

If the object completes one oscillation in 2 sec. then its period is 2 sec, T = 2.

The phase angle can now be determined.

So, the general equation of motion is

When it will have covered a distance of 9 inches, it is at the equilibrium position. From A to 0, from 0 to -A, then from -A to 0 again to complete 9 inches, since A = 3.

Since we know that a full oscillation is completed in 2 sec. than 3/4 oscillation should be completed in 1.5s.

So, equation of motion at that instant is