Problem 12E

A mass of 1 slug is suspended from a spring whose spring constant is 9 lb/ft. The mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of Find the times at which the mass is heading downward at a velocity of 3 ft/s.

Solution

In this question it is given that A mass of 1 slug is suspended from a spring whose spring constant is 9 lb/ft. The mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of, we have to find the times at which the mass is heading downward at a velocity of 3 ft/s.

Step 1

The above conditions can be written in the form of differential equation as

Here

=>

and

Here it is given that mass is heading downwards with a velocity of 3ft/s

So

=>

Therefore times the mass is heading downwards with the velocity of 3ft/s.