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The frequency of oscillation of a mass m suspended by a spring is `v_(1)`. If the length of the spring is cut to on-half, the same mass oscillates with frequency `v_(2)`. Determing the value of `v_(2)//v_(1)`. |
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Answer» Let the full spring be the combination of two springs in series, each of force constant k. Then, in case (i), The effective spring constant `(K_(1))` is given by `K_(1)=(kxxk)/(k=k)=(k)/(2)` Frequency of oscillation, `v_(1)=(1)/(2pi) sqrt((K_(1))/(m))=(1)/(2pi)sqrt((k)/(2m))` ...(i) In case (ii), When the spring is cut to one-half, the effective spring constant `K_(2)=k`. Frequency of oscillation, `v_(2)=(1)/(2pi)sqrt((K_(2))/(m))=(1)/(2pi)sqrt((k)/(m))` ...(ii) `:. v_(2)//v_(1)=sqrt(2)` |
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