GATE2018-1-7

Question

The equation of motion for a spring-mass system excited by a harmonic force is $M\ddot{x} + K x = F \cos(\omega t)$, where $M$ is the mass, $K$ is the spring stiffness, $F$ is the force amplitude and $\omega$ is the angular frequency of excitation. Resonance occurs when $\omega$ is equal to

• A. $\sqrt{\dfrac{M}{K}} \\$
• B. $\dfrac{1}{2 \pi} \sqrt{\dfrac{K}{M}} \\$
• C. $2 \pi \sqrt{\dfrac{K}{M}} \\$
• D. $\sqrt{\dfrac{K}{M}}$