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

AI Thread Summary
The discussion revolves around a critically damped forced harmonic oscillator with a 9 kg mass and a spring constant of 4 N/m, subjected to an external force of 10sin(3t) N. The damping coefficient is 12 N-sec/m, leading to the classification of the system as critically damped. Participants are tasked with determining the displacement y(t) of the mass over time, as well as identifying both the transient and steady-state solutions. The original poster expresses confusion about calculating the displacement despite recognizing the system's damping condition. The conversation emphasizes the need for clarity in solving forced harmonic oscillator problems.
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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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