A bob of mass 0.1 kg is attached to a spring of natural length l₀=0.1 m. k₁=0.009 N m⁻¹ for ll₀ and k₂=0.016 N m⁻¹ for l

Question

A bob of mass 0.1 kg is attached to a spring of natural length l₀=0.1 m. k₁=0.009 N m⁻¹ for l>l₀ and k₂=0.016 N m⁻¹ for l<l₀. It is released from l=0.15 m. If full period is T=nπ s, find the nearest integer n.

Physics · Simple Harmonic Motion

JEE Advanced 2021

G1 Physics · Accepted Answer

The spring has different constants on the two sides of its natural length. For extension side, half-cycle time is π√(m/k₁); for compression side it is π√(m/k₂). Thus T=π√(0.1/0.009)+π√(0.1/0.016)=π(10/3+5/2)=35π/6≈5.83π s. Therefore n≈5.83 and the nearest integer is 6.