Damped Resonance Frequency — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Damped Resonance Frequency This formula determines the resonance frequency for a damped harmonic oscillator when subjected to an external driving force. Start with the equation of motion for a damped, driven oscillator: m d 2x dt 2 + b dx dt + kx = F 0 ( t). Determine the steady-state amplitude A( ) by solving the differential equation. The resonance frequency r is the frequency that maximizes this amplitude A( ). Differentiate A( ) with respect to and set the derivative to zero to find r. The term under the square root must be non-negative: 0 2 b 2 2m 2 The system must be undergoing damped oscillations. Confusing the resonance frequency ( r) with the natural frequency ( 0). Assuming the resonance frequency is always equal to the natural frequency (this is only true if damping b=0). Incorrectly applying the damping coefficient (b) in the formula (it must be squared and divided by mass terms).