The frequency of oscillation of a mass suspended by a spring is . If the length of the spring is cut to half, the same

Question

The frequency of oscillation of a mass $m$ suspended by a spring is $f_{1}$ . If the length of the spring is cut to half, the same mass oscillates with frequency $f_{2}$ . The value of $\frac{f_{2}}{f_{1}}$ is ______. [2026]

Smart Achievers · Accepted Answer

(3)

$f = \frac{1}{2 π} \sqrt{\frac{k}{m}}$

$k l = constant$

$k_{1} l = k_{2} \frac{l_{2}}{2} \Rightarrow k_{2} = 2 k_{1}$

$f \propto \sqrt{k}$

$\frac{f_{2}}{f_{1}} = \sqrt{\frac{k_{2}}{k_{1}}} = \sqrt{\frac{2 k_{1}}{k_{1}}} = \sqrt{2}$

Solution

Q.
The frequency of oscillation of a mass $m$ suspended by a spring is $f_{1}$ . If the length of the spring is cut to half, the same mass oscillates with frequency $f_{2}$ . The value of $\frac{f_{2}}{f_{1}}$ is ______. [2026]

1 $1$

2 $2$

3 $\sqrt{2}$

4 $\sqrt{3}$

Ans.
(3)

$f = \frac{1}{2 π} \sqrt{\frac{k}{m}}$

$k l = constant$

$k_{1} l = k_{2} \frac{l_{2}}{2} \Rightarrow k_{2} = 2 k_{1}$

$f \propto \sqrt{k}$

$\frac{f_{2}}{f_{1}} = \sqrt{\frac{k_{2}}{k_{1}}} = \sqrt{\frac{2 k_{1}}{k_{1}}} = \sqrt{2}$

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