Displacement Equation Of Shm — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Displacement Equation of SHM Valid for Simple Harmonic Motion where the restoring force is directly proportional to the displacement and acts in the opposite direction (Hooke's Law), without damping. Start with Newton's Second Law: F = ma. Substitute restoring force F = -kx. Express acceleration a as d 2x/dt 2. Form the differential equation: m(d 2x/dt 2) + kx = 0. Define omega 2 = k/m. Solve the second-order homogeneous differential equation d 2x/dt 2 + omega 2 x = 0. General solution is x(t) = A cos(omega t + phi). Motion must be one-dimensional. Restoring force must be linear (F = -kx). No friction or damping forces (ideal system). Confusing angular frequency (rad/s) with frequency (Hz). Calculating trigonometric functions using degrees instead of radians. Assuming the phase constant phi is always zero. Confusing displacement x with distance traveled.