Question

Asked Jun 24, 2019

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Mechanical Vibrations (differential equations)

A mass weighing 4 pounds is attached to a sping whose constant is 2lb/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point one foot above the equilibrium position with a downward velocity of 8ft/s. Determine the time at which the mass passes through the equilibrium position.

Step 1

Let *m* be the mass attached, *k* be the spring constant and let *b* be a positive damping constant.

Then, by Newton’s second law for the system is:

Step 2

Where *x*(*t*) is the displacement from the equilibrium position.

Now, determine the equation of motion.

Step 3

Now, put m=1/8 slugs, *k*=2 lb/ft and *b*=1 into t...

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