A harmonic oscillator has a spring constant k and a mass m. It has a natural osc

Question

A harmonic oscillator has a spring constant k and a mass m. It has a natural oscillation frequency w. The oscillator is hooked up to an external force that is periodic with frequency wf. The external force is adjusted so that wsw and it is in resonance with the oscillator. The frequency of the external force is then changed to wf- 3w. It is attached to a set of harmonic oscillators with different values of k and m. With which of the following oscillators will the external force be in resonand e! (a) (3k, m) (b) (32k, 4m) (c) (16k, 4m) (d) (9k, 3m) (e) (27k, 3m)

Explanation / Answer

w = sqrt(k/m)

now k/m = w2

finally for resonance, k'/m' = (w')2 = (3w)2 = 9w2 = 9k/m

=> k'/m' = 9k/m

=> a) k'/m' = 3k/m

b) k'/m' = 32k/4m = 8k/m

c) k'/m' = 16k/4m = 4k/m

d) k'/m' = 9k/3m = 3k/m

e) k'/m' = 27k/3m = 9k/m = required => answer is e) (27k,3m)

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