First slide

Simple hormonic motion

Question

A block is suspended by a spring and the deflection produced in the spring is 2 cm when the block is slightly pulled downward and released, its time period is found to be 1 second. When another block is suspended by the same spring, its elongation is found to be 8 cm. Now if this block is slightly pulled downward and released, what will be its time period?

Easy

A

4 sec
B

2 sec
C

0.5 sec
D

8 sec

Solution

$m g = K . x \Rightarrow \frac{m}{K} = \frac{x}{g}$
Now $T = 2 π \sqrt{\frac{m}{K}} = 2 π \sqrt{\frac{x}{g}}$
$\Rightarrow x = \frac{g . T^{2}}{4 π^{2}} \Rightarrow x α T^{2}$
$∴ \frac{T_{2}^{2}}{T_{1}^{2}} = \frac{x_{2}}{x_{1}} \Rightarrow \frac{T_{2}}{1} = \sqrt{\frac{8}{2}} \Rightarrow T_{2} = 2 second$

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