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 m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass rn is increased by I kg, the time period of oscillations becomes 5 s. The value of m in kg is

Moderate

A

$\frac{16}{9}$
B

$\frac{9}{16}$
C

$\frac{3}{4}$
D

$\frac{4}{3}$

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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