An undamped oscillator with natural angular frequency is driven so that its…
PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Oscillations, Waves & Acoustics · Simple, damped and driven oscillations
Mathematical Methods for Physics, Ch Higher-order linear equations, the Wronskian and variation of parameters
Problem
An undamped oscillator with natural angular frequency ω0=3rads−1 is driven so that its displacement x(t) obeys x¨+9x=ttan3t, valid for ∣3t∣<π/2. Without carrying out the integration, decide whether the method of undetermined coefficients (guessing a trial function) can produce a particular integral for this drive. State the reasoning, and name the method that will work if guessing fails.