This problem is an example of critically damped harmonic motion. A mass m=6kg is attached to both a spring with spring constant k=96N/m and a dash-pot with damping constant c=48N?s/m . The ball is started in motion with initial position x0=5m and initial velocity v0=?24m/s . Determine the position function x(t) in meters. x(t)= Graph the function x(t) . Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected ( so c=0 ). Solve the resulting differential equation to find the position function u(t). In this case the position function u(t) can be written as u(t)=C0cos(?0t??0). Determine C0, ?0 and ?0. C0= ?0= ?0= (assume 0??0<2? ) Finally, graph both function x(t) and u(t) in the same window to illustrate the effect of damping.
