JEE Main 2026 Apr 6 Shift 2, Physics Q11: SHM in Spring-Mass System

JEE Main2026Apr 6, Shift 2Physics

A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maximum energy in the spring are ______ Hz and ______ J, respectively. (Take $g = 10$ m/s $^{2}$ )

A
$\frac{5 50}{π}$ and $8 \times 1 0^{- 3}$
B
$\frac{5 50}{π}$ and $8$
C
$1050$ and $2 \times 1 0^{- 3}$
D
$\frac{5 50}{π}$ and $16 \times 1 0^{- 3}$

Solution

Spring constant from static stretch: $k x_{0} = m g$ $\Rightarrow$ $k = \frac{0.2 \times 10}{2 \times 1 0 ^{- 3}} = 1000$ N/m.

Frequency: $f = \frac{1}{2 π} \frac{k}{m} = \frac{1}{2 π} \frac{1000}{0.2} = \frac{1}{2 π} 5000 = \frac{5 50}{π}$ Hz.

Maximum energy with amplitude $A = 2$ mm $= 2 \times 1 0^{- 3}$ m (about the equilibrium position):

$E_{ma x} = \frac{1}{2} k A^{2} = \frac{1}{2} (1000) (2 \times 1 0^{- 3})^{2} = 2 \times 1 0^{- 3}$ J.

Including the static deformation, total elastic PE stored at lowest point uses extension $= 2 + 2 = 4$ mm:

$E_{s p r in g, ma x} = \frac{1}{2} (1000) (4 \times 1 0^{- 3})^{2} = 8 \times 1 0^{- 3}$ J.

This matches option (1): $\frac{5 50}{π}$ Hz and $8 \times 1 0^{- 3}$ J.

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JEE Main 2026 Apr 6 Shift 2, Physics Q11: SHM in Spring-Mass System

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