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

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/s

for the acceleration due to gravity.)

* x*(

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

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) =
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