This problem is an example of critically damped harmonic motion.

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(ω0t−α0). Determine C0, ω0 and α0. C0= ω0= α0= (assume 0≤α0<2π ) Finally, graph both function x(t) and u(t) in the same window to illustrate the effect of damping.

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Colby Messinger answered 1 year ago

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