JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Elasticity & SHM

A mass

m

attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of oscillation increases by one second, the value of mass

m

is ____ kg.

Answer: 1

Solution

For a spring-mass system

T = 2 π \frac{m}{k}

, so the ratio of the two periods is

\frac{T}{T ^{'}} = \frac{m}{m + 3}

. The period rises from 1 s to 2 s, giving

\frac{m}{m + 3} = \frac{1}{2}

, so

\frac{m}{m + 3} = \frac{1}{4}

and

4 m = m + 3

. The mass is

m = 1

kg.

JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Integer answer

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