**Problem 7:** A block weighing 4 kg extends a spring by 0.16 m from its un-stretched position. The block is removed and a 0.50 kg body is hung from same spring. If the spring is now stretched and released, what is its period of vibration?

**Solution**

**Given data ** Mass of the body hung first, m_{1} = 4 kg Displacement = 0.16 m

Mass attached for the 2^{nd} time = m_{2} = 0.50 ka

**Required **Time period =?

**Formula**

**Theory **We donâ€™t know the value of k in the formula. This can be calculated from the data when a mass of 4 kg is hung to it. Since, F = kx, therefore, k = F/x. Force in this case is the weight of the 4 kg mass, i-e, F = W = mg

So

Now put this value of k in the formula to get the time period.

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