Driven Oscillator Amplitude And Phase — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Driven Oscillator Amplitude and Phase This formula describes the steady-state amplitude and phase shift of a mass attached to a spring and damper system when subjected to an external sinusoidal 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) . Assume a steady-state solution of the form x(t) = X( ) ( t - ) . Substitute the assumed solution into the differential equation and solve for the amplitude X( ) and phase ( ) . The maximum amplitude occurs at the resonant frequency r = k/m (for small damping b ). m > 0 k 0 b 0 0 Assuming the amplitude is maximized at the natural frequency 0 = k/m regardless of damping (damping lowers the peak). Confusing the driving frequency with the natural frequency 0 . Forgetting that the phase shift depends on the ratio of damping to stiffness terms.