Velocity Displacement Relation In Shm — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Velocity-Displacement Relation in SHM Valid for Simple Harmonic Motion where energy is conserved (no damping). Applies to springs, pendulums (small angle), and projection of uniform circular motion. Express position as x(t) = A cos(wt + phi). Differentiate to find velocity v(t) = -Aw sin(wt + phi). Use the trigonometric identity sin 2(theta) + cos 2(theta) = 1 to substitute sin(wt+phi) with sqrt(1 - (x/A) 2). Simplify the expression to derive v = w sqrt(A 2 - x 2). |x| <= A Motion is undamped simple harmonic Believing velocity is maximum when displacement is maximum (velocity is actually zero at max displacement). Assuming the relationship is linear (it is quadratic/elliptical). Forgetting that displacement x is measured from equilibrium, not the start point.