Question

A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to

sqrt(2) times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 9 ft/s. (Use

g = 32 ft/s² for the acceleration due to gravity.)

x(t) =

Find the time at which the mass attains its extreme displacement from the equilibrium position.

t =

What is the position of the mass at this instant?

The extreme displacement is x = ____ feet.

Answer 1

Differential equation is

So

Characteristic equation is (repeated root)

So that

Initial conditions imply

So that

For max displacement, so that

Therefore, the time is seconds and the displacement is feet (without negative sign)

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