A particle of mass 0.50 kg executes simple harmonic motion under force F = -50(N m⁻¹)x. The time period of oscillation is x/35 s. The value of x i s ______. (Given π = 22/7)
Physics · Simple Harmonic Motion · time period of linear shm
JEE Mains 2024 09 Apr Evening Shift

Question

A particle of mass 0.50 kg executes simple harmonic motion under force F = -50(N m⁻¹)x. The time period of oscillation is x/35 s. The value of x i s ______. (Given π = 22/7)

G1 Physics · Accepted Answer

For SHM: F = -kx Given: k = 50 N/m m = 0.50 kg Angular frequency: ω = √(k/m) = √(50/0.5) = √100 = 10 rad/s Time period: T = 2π/ω = 2π/10 = π/5 Using π = 22/7: T = 22/35 s Comparing with: T = x/35 s we get: x = 22