A mass weighing 500 g stretches a spring 10 cm. The mass is pushed upward, contracting the spring a distance of 5 cm, and then set in motion with a downward velocity of 4 m/s. Assume there is no damping. a) Set up the initial value problem (differential equation). b) Solve the equation to find the position of the mass y at any time t. c) Find the frequency, period, amplitude and phase of the oscillation.

A mass-spring system obeys simple harmonic motion according to the function f(t) = 2 cos (). Blank 1: Find the amplitude of the motion. Blank 2: Find the frequency of the motion.

A mass of 1 kg is attached to a spring and a damper, set in motion, and observed to move as x(t) = 3 e-2t sin(3t). Determine the spring constant k (in kg/s²) and the damping constant c (in kg/s), where c= = 2 mwo S.

When a car hits a certain bump on the road, a shock absorber on the car is compressed a distance of 5 in., then released. The shock absorber vibrates in damped harmonic motion with a frequency of 3 cycles per second. The damping constant for this particular shock absorber is 2.5.How long does it take for the amplitude of the vibration to decrease to 0.2 in?