What is the displacement of a critically damped forced harmonic oscillator?

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SUMMARY

The discussion centers on a critically damped forced harmonic oscillator involving a 9 kg mass attached to a spring with a spring constant of 4 N/m and a damping coefficient of 12 N-sec/m. The external force applied is F(t) = 10sin(3t) N. The system is confirmed to be critically damped, and the user seeks assistance in determining the displacement function y(t) and identifying both the transient and steady-state solutions.

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  • Basic principles of forced oscillations and external forces in mechanical systems.
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Spring Constant Question...please help!

Hello .I have an annoying question here...A 9 kg mass attached to a spring with spring constant 4 N/m. At time t=0 and external force F(t)=10sin(3t) N is applied to the mass. The damping coefficient for the system equals 12 N-sec/m.

NOTE: If y(t) represents the deviation at time t of the mass from the equilibrium position then y(0)=0 and y'(0)=01) Determine if the system is over damped, critically damped, or under damped

2) find the displacement y(t) of the mass at time t

3) Identify the transient solution and the steady state solutionI've stared at this for a while now and I have no idea what to do...I know it's critically damped but I can't figure out the displacement.
 
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Look up "forced harmonic oscillator".
 

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