laplace transformation

Question

A mass weighing 4 pounds is attached to a spring whose 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 a point 1 foot below the equilibrium position with a downward velocity of 8 ft/s. Find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant?

Answer 1

The sum of forces on the mass = 4/gy''=-2y-y'-4 ... find the transform of this equation to be y(s)=(-6s²-gs+1)/(sg)/(s²+sg/4+g/2). Find the inverse transform to be y(t)= -37e^-4t+35E^-4.05t+.062. To find the maximum of y(t) find y' and set =0, then solve for t to be .375 seconds