5. Given a damped-spring system. The spring has a mass of m=0.50kg, and force constant of k=0.50N/m. The damping constant is beta=0.5rad/s. The spring starts from rest at an initial position of x 0=0.50 meters.
a. Is this system under-, critical-, or over-damped?
b. Determine the specific solution of motion for this system, and plot for a span of 15 seconds.
c. What is the resonance frequency for this system if the natural frequency is held constant?
d. What is the Q-factor of the oscillator at the resonance frequency in (c)?