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Mechanical Engineering QUESTION #2441
Question 1
For forced undamped vibrations, the equation of motion \(m\ddot{x}+kx=F_0\sin pt\) has a particular solution (forced response amplitude) of:
  • \(X = \frac{F_0/k}{1-(p/\omega_n)^2}\) for \(p\neq\omega_n\)✔️
  • \(X = \frac{F_0}{k}\)
  • \(X = \frac{F_0}{k}\cdot\frac{p}{\omega_n}\)
  • \(X = \frac{F_0 k}{p^2}\)
Correct Answer Explanation
The particular solution amplitude is \(X=\frac{F_0/k}{1-(p/\omega_n)^2}=\frac{x_{st}}{1-(p/\omega_n)^2}\). As \(p\to\omega_n\), \(X\to\infty\) (resonance).