Driven Damped Oscillator Equation — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Driven Damped Oscillator Equation This equation describes the motion of a mass attached to a spring, subjected to damping and an external sinusoidal driving force. Start with Newton's Second Law: F = ma. Identify the forces: Restoring force ( -kx ), Damping force ( -b dx dt ), and External force ( F(t) ). Set the external force to a sinusoidal function: F(t) = F 0 ( t) . Combine all forces into the differential equation form. m > 0 b >= 0 k > 0 F 0 0 t 0 Confusing the natural frequency ( 0 = k/m ) with the driving frequency ( ). Assuming the system oscillates at the natural frequency even when a strong external force is applied. Forgetting that damping ( b ) always dissipates energy from the system.