a) a spring attached to a ceiling is stretched 1.96 m by a 4 kg mass. finad the hooke's law spring constant, k. (use g=9.8 m/sec^2 for the acceleration due to gravity)
b) if the mass is set into motion in a medium thta imparts a damping force equal to 16 times the velocity, find the differential equation for the position, x(t), of the mass as a function of time.
c) solve the differential equation from part b
d) determine the equation of motion if the mass is initially released from a postion 1/2 m below equilibrium with an upward velocity of 1.866m/s3 + 2 m
e)identify the period, phase shift, phase angle, frequency and initial amplitude.