A mass m attached to free end of a spring executes SHM with… — JEE Main 2023 Physics PYQ

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

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.

Show answer and solution

Answer: 1

Solution

For a spring-mass system, T = 2π√(m/k).

T₁ = 1 s → 1 = 2π√(m/k)
T₂ = 2 s → 2 = 2π√((m+3)/k)

Dividing: 2/1 = √((m+3)/m) → 4 = (m+3)/m → 4m = m+3 → 3m = 3 → m = 1 kg

[JEE Main 2023 · 24 Jan · Shift 2]

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