Two springs of force constants K 1 and K 2 , respectively, are connected to a mass m , as shown. The frequency of oscillation of the mass is f . If both K 1 and K 2 are made four times their original

Question

Two springs of force constants K 1 and K 2 , respectively, are connected to a mass m , as shown. The frequency of oscillation of the mass is f . If both K 1 and K 2 are made four times their original values, the frequency of oscillation becomes

TestHub · Accepted Answer

In the given figure, two springs are connected in parallel. Therefore, the effective spring constant is given by

$K_{eff} = K_{1} + K_{2}$

<!--{cke_protected}{C}%3C!%2D%2D%0A%09%09%40page%20%7B%20margin%3A%202cm%20%7D%0A%09%09P%20%7B%20margin-bottom%3A%200.21cm%20%7D%0A%09%2D%2D%3E--<img src="https://storage.googleapis.com/mathpix/nta_abhyas/neet/images/content_2524.1.png" data-cke-saved-src="https://storage.googleapis.com/mathpix/nta_abhyas/neet/images/content_2524.1.png" style="width: 669px; height: 183px;" alt="">Frequency of oscillation,

$f = \frac{1}{2 π} \sqrt{\frac{K_{eff}}{m}} = \frac{1}{2 π} \sqrt{\frac{K_{1} + K_{2}}{m}}$ ...........(i)

As $K_{1}$ and $K_{2}$ are increased by four times

New frequency,

$f^{'} = \frac{1}{2 π} \sqrt{\frac{4 (K_{1} + K_{2})}{m}} = 2 f$ ( using (i) )

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