JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Elasticity & SHM

The velocity of a particle executing simple harmonic motion along x-axis is described as

v^{2} = 50 - x^{2}

, where x represents displacement. If the time period of motion is

\frac{x}{7}

s, the value of x is _____ .

Answer: 44

Solution

For simple harmonic motion

v^{2} = ω^{2} (A^{2} - x^{2})

. Comparing with

v^{2} = 50 - x^{2}

gives

ω^{2} = 1

, so

ω = 1

rad/s and the time period is

T = \frac{2 π}{ω} = 2 π

s. Setting

2 π

equal to the stated period and using

π = \frac{22}{7}

gives the required value

14 π = 44

JEE Main · 2026 · 04 Apr 2026 · Shift 1 · Integer answer