A particle executes simple harmonic motion along the x-axis and satisfies v² = 50-x², where x is displacement and v is speed in consistent SI units. If the time period of the motion is X / 7 seconds, find X to the nearest integer.
Physics · Simple Harmonic Motion · Time Period of Linear Simple Harmonic Motion
JEE Mains 2026 4 April Morning Shift

Question

A particle executes simple harmonic motion along the x-axis and satisfies v² = 50-x², where x is displacement and v is speed in consistent SI units. If the time period of the motion is X / 7 seconds, find X to the nearest integer.

Physics · Simple Harmonic Motion · Time Period of Linear Simple Harmonic Motion

JEE Mains 2026 4 April Morning Shift

G1 Physics · Accepted Answer

For simple harmonic motion, v² = ω²(A²-x²). Comparing with v² = 50-x², the coefficient of x² gives ω² = 1, so ω = 1 rad·s⁻¹. Hence the time period is T = 2π ÷ ω = 2π s. Given, T = X ÷ 7 s. Therefore, X ÷ 7 = 2π, X = 14π ≈ 43.98. To the nearest integer, X = 44.