(Solved):   III. (15 points) A mass of 1 slug, when attached to a spring, stretches it 2 feet and then ...

 

III. (15 points) A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in equilibrium position. At l = 0, an external force equal to f(1) = 8 sin(40) is applied to the system. 1. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity (the mass is released from equilibrium with no initial velocity). 2. Is the system underdamped, over-damped, or critically damped and why? 3. In the long-run discuss the behavior of the motion of the system (i.e solution). Include a sentence interpreting your conclusion.