First slide

Simple hormonic motion

Question

A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass rt is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of min kg is :

Easy

A

16/9
B

9/16
C

3/4
D

4/3

Solution

$T = 2 π \sqrt{\frac{m}{k}} 3 = 2 π \sqrt{\frac{m}{k}} . . . . (1) 5 = 2 π \sqrt{\frac{m + 1}{k}} . . . . . (2) \frac{{(1)}^{2}}{{(2)}^{2}} \Rightarrow \frac{9}{25} = \frac{m}{m + 1} \Rightarrow m = \frac{9}{16}$

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