Question

Two springs have force constants in ratio 4;9 their time periods are in the ratio

Answer 1

Answer:

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Answer 2

Given:

It is given that springs have force constants in ratio 4:9

Answer:

We have the relation for a spring-mass system as

$T=2\pi \sqrt{\frac{m}{k} }$

In above relation, if $2\pi$ and $m$ are considered to be constants

$T\propto\frac{1}{\sqrt{k} }$

so we can write,  $\frac{T_1}{T_2} = \sqrt{\frac{k_2}{k_1} }$

It is given that  $\frac{k_2}{k_1} =\frac{9}{4}$

$\frac{T_1}{T_2} = \sqrt{\frac{9}{4} }$

$\frac{T_1}{T_2} = \frac{3}{2}$

∴The time periods are in the ratio 3:2