Amass weighing 16 lb stretches a spring 3 in. the mass is attached to a viscous damper with a damping constant of 2 lb-s/ft. if the mass is set in motion from its equilibrium position with a downward velocity of 2 in/s, find its position u at any time t. assume the acceleration of gravity g=32 ft/s2.

Explanation:

Our values given are,

Ramping constant

By this way we can calculate k and m.

We can now create the differential equation, which is given by,

The initial conditions are:

*Note that the velocity war given in inches and transformated to feet.

With that we can create our characteristic equation:

With two roots

Our general solution of the Differential equation is then,

Applying the initial conditions,

The position of u at any time t is,

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