First slide

Applications of SHM

Question

A mass m is suspended from a spring of length l and force constant K. The frequency of vibration of the mass is f₁ . The spring is cut into two equal parts and the same mass is suspended from one of the parts. The new frequency of vibration of mass is f₂ . Which of the following relations between the frequencies is correct

Moderate

A

$f_{1} = \sqrt{2} f_{2}$
B

$f_{1} = f_{2}$
C

$f_{1} = 2 f_{2}$
D

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

Solution

When spring is cut into two equal parts then spring constant of each part will be 2K and so using $n \propto \sqrt{K}$ , new frequency will be $\sqrt{2}$ times i.e. $f_{2} = \sqrt{2} f_{1}$ .

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