Consider a damped harmonic oscillator. The amplitude of the oscillation of a mass hanging by a spring is: y(t)=exp((R2)t)sint where y(t) is the amplitude (height) of the spring at time t,2F2R24 is the square of the natural frequency of oscillation with damping, 2Fk,k is the spring constant, and R is the damping coefficient. Set a constant k=1 and vary R from 0 to 2 in increments of 0.25. Plot y versus t (how the amplitude changes with time) for t=0 to 30 for each case