Q.

A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency (in Hz) of vibration of the 8 kg block is _____.

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answer is 0.5.

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Detailed Solution

If 1 kg block attached to a spring vibrates with a frequency,v=12πkm=1Hz⇒ k=4π2Nm−1When two springs are attached in parallel to an 8 kg block, thenkeq=k+k=2kFrequency, v′=12πkeqm′=12π2k8=12π2×4π28=12Hz=0.5Hz
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