Q.11 The differential equation of linear S.H.M. in SI units is d²x/dt² = -36x . Calculate its frequency and periodic time.

Answer: n ≈ 0.955 Hz, T ≈ 1.047 s Comparing with d²x/dt² = -ω²x : ω² = 36 , so ω = 6 rad/s. n = ω/2π = 6/2×3.142 = 0.9548\ Hz T = 1/n = 2π/ω = 6.284/6 = 1.047\ s

The differential equation of linear S.H.M. in SI units is \(\dfrac{d^2x}{dt^2} = -36x\). Calculate its frequency and periodic time.

Q.11 The differential equation of linear S.H.M. in SI units is \(\dfrac{d^2x}{dt^2} = -36x\). Calculate its frequency and periodic time.

Doubtly Asked 28 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

1 answer

Best answer

Answer: \(n \approx 0.955\) Hz, \(T \approx 1.047\) s

Comparing with \(\dfrac{d^2x}{dt^2} = -\omega^2x\): \(\omega^2 = 36\), so \(\omega = 6\) rad/s.

\[n = \frac{\omega}{2\pi} = \frac{6}{2\times3.142} = 0.9548\ \text{Hz}\]\[T = \frac{1}{n} = \frac{2\pi}{\omega} = \frac{6.284}{6} = 1.047\ \text{s}\]

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

Was this answer helpful?

The differential equation of linear S.H.M. in SI units is \(\dfrac{d^2x}{dt^2} = -36x\). Calculate its frequency and periodic time.

1 answer

Your answer