Driven Oscillator Velocity And Acceleration — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Driven Oscillator Velocity and Acceleration Describes the maximum (amplitude) velocity and acceleration of a damped harmonic oscillator driven by an external force, assuming steady-state conditions. 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 - ) . Calculate the derivatives of x(t) to find the velocity v(t) and acceleration a(t) . Determine the amplitudes V( ) and A( ) by analyzing the coefficients of the driving force and damping terms. 0 Confusing the maximum velocity/acceleration amplitudes with the instantaneous values. Assuming the relationship holds for the transient (initial) phase of oscillation, rather than the steady state. Forgetting that X( ) itself is frequency-dependent and reaches its maximum at resonance.