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Mechanical Engineering QUESTION #2453
Question 1
The general solution for forced damped vibration \(x=x_1+x_2\) consists of:
  • Only the steady-state component \(x_2=B_2\sin(pt-\phi)\)
  • Transient free-damped oscillation \(x_1=B_1e^{-\alpha t}\sin(\omega_d t+\psi)\) PLUS steady-state harmonic \(x_2=B_2\sin(pt-\phi)\)✔️
  • Only the transient component that decays to zero
  • A constant DC offset plus a harmonic
Correct Answer Explanation
The complete solution is \(x=x_1+x_2\): the transient part \(x_1=B_1e^{-\alpha t}\sin(\omega_d t+\psi)\) decays with time; the steady-state part \(x_2=B_2\sin(pt-\phi)\) persists indefinitely.