1.a) Suppose you have a block resting on a horizontal smooth surface. The block

Question

1.a) Suppose you have a block resting on a horizontal smooth surface. The block (with a mass of 'm') is attached to a horizontal spring (spring constant 'k' (N/m)), which is fixed at one end. The spring can be compressed and stretched. The mass is pulled to one side and then released. What is the formula required to calculate the period of the oscillation of the mass? If m = 100 g, and k = 150 N/m, what are the period and frequency of the oscillation?

b) If the block of mass 'm' were replaced with a block 4 times more massive, by what factor would the period change? Would the period be longer or shorter?

Explanation / Answer

Given Mass , m = 0.1 kg Spring constant , k = 150N/m a)Time period, T = 2 k/m                         = 2 *3.14 * 150N/m / 0.1kg                      T = 243.22 s Frequency , f = 1/T = 1/243.22 s                      = 0.0041 Hz b) If mass is 4m , then                    T 1/m                     T1 /T2 = 4m / m                         T2 = 1/2T1 Period reduces by 1/2 of its initial period

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