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Mechanical Engineering QUESTION #2454
Question 1
The Rayleigh (energy) method for approximating the fundamental natural frequency equates:
  • Maximum kinetic energy to maximum potential energy: \(T_{max} = V_{max}\) giving \(\omega_n^2 = k/m\)✔️
  • Mean kinetic energy to mean potential energy
  • Damping energy to spring potential energy
  • Total energy to the product of mass and stiffness
Correct Answer Explanation
Rayleigh's method: for conservative systems in harmonic motion, maximum kinetic energy \(T_{max}=\frac{1}{2}m(\omega_n X)^2\) equals maximum potential energy \(V_{max}=\frac{1}{2}kX^2\). Setting \(T_{max}=V_{max}\): \(\omega_n^2=k/m\).