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, m₁ = 4 kg                 Displacement = 0.16 m

                                      Mass attached for the 2^nd time = m₂ = 0.50 ka

Required                         Time period =?

Formula

Theory                      We don’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.