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?
Given data Mass of the body hung first, m1 = 4 kg Displacement = 0.16 m
Mass attached for the 2nd time = m2 = 0.50 ka
Required Time period =?
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
Now put this value of k in the formula to get the time period.