A mass oscillates with \( v = -15 \cos (3t) \) (in m/s). What is its amplitude?
**Velocity and acceleration in SHM** follow from differentiation, showing 90° phase lead of v over x and 180° for a over x. At mean position x=0, a=0, v=±ωA maximum; at extremes x=±A, v=0, a=∓ω²A maximum magnitude, illustrating energy conversion. Velocity: v = -ω A sin (ω t) , but given v = -15 cos (3t) . ω = 3 s⁻¹, vₘₐₓ = ω A = 15 ⇒ A = (15/3) = 5 m . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 5 m follows, reflecting SHM dependence on amplitude A, ω and system parameters.
Ref: NCERT > Physics Book > Oscillations > Displacement, Velocity and Acceleration in SHM
