A particle in SHM has \( x = 4 \sin (3t) \) (in m). What is its speed at \( x = 2 \, \text{m} \)?
**SHM condition** is linear restoring force and inertia producing sinusoidal time dependence. Motions violating a = -ω² x, such as uniform circular motion, are periodic without oscillation about fixed point, highlighting classification criteria for NCERT. Velocity: v = ± ω √(A² - x²) . A = 4 m, ω = 3 s⁻¹, x = 2 m . v = 3 √(4² - 2²) = 3 √(16 - 4) = 3 √(12) = 3 × 2√(3) ≈ 10.39 m/s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 10.39 m/s follows,
Ref: NCERT > Physics Book > Oscillations > Periodic Motion and SHM Basic Concepts