Structural Dynamics MCQ with answer and solution

Concept

In Rayleigh's method, maximum kinetic energy (at mean position) is equated to maximum potential energy (at extreme position) to find natural frequency.

Formula

KE_max = PE_max; ω = √(k/m)

Step-by-step solution

1. In free vibration, there is no energy loss (undamped system). 2. At the mean position, speed is maximum, so KE is maximum and PE is zero. 3. At the extreme position, speed is zero, so PE is maximum and KE is zero. 4. Rayleigh's method puts KE_max = PE_max. 5. This gives the natural frequency of the system.

Explanation

In Rayleigh's method, we use conservation of energy. The maximum kinetic energy at the mean position is equal to the maximum potential energy at the extreme position. From this we find the natural frequency.

Why the other options are wrong

B: 'Energy method' is a general name, not the specific named method asked here. C: Equilibrium method uses force balance, not energy. D: Stress-strain method is not a vibration method.

Shortcut

Max KE = Max PE means Rayleigh's method.

Common mistake

Choosing 'Energy method' because the word energy appears in the question.