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Question

A spring system has \( m = 0.25 \, \text{kg}, k = 100 \, \text{N/m}, A = 8 \, \text{cm} \). What is the
potential energy at \( x = 4 \, \text{cm} \)?

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Explanation

**Energy distribution** shows maximum kinetic at equilibrium and maximum potential at extremes, sum constant. This relation enables calculation of amplitude, velocity at any displacement via v = ±√(2(E-U)/m), and understanding of energy storage in oscillating system for NEET problems. Potential energy: U = (1/2) k x² . k = 100 N/m, x = 0.04 m . U = 0.5 × 100 × (0.04)² = 0.5 × 100 × 0.0016 = 0.08 J . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 0.08 J follows, reflecting SHM dependence on amplitude A, ω and system parameters.

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