A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from rest from a point 8 inches above the equilibrium position. Give the initial conditions. Find the equation of motion. (use g = 32 ft/s^2 for acceleration due to gravity. Assume t is measured in seconds. ) 

Find the equation of motion? x(t) = 

A mass weighing 4 pound is attached to a spring whose spring constant is 2 lb/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from 1 foot above the equilibrium position with a downward velocity of 14 ft/s. Determine the time at which mass passes through the equilibrium position. (Use g = 32 ft/s^2 for acceleration due to gravity.)

Find the time (in s) after mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position.

What is the position of the mass at this instant?

A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position, Starting at t = 0, an external force equal to f(t) = 6sin(4t) is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. (Use g = 32 ft/s^2 for the acceleration due to gravity.)