  We apply perturbative techniques to a driven undamped sinusoidal oscillator
at resonance. The angular displacement, $\theta$, obeys the dynamics
$\Ddot{\theta} + \omega^{2} \sin{\theta} = H\cos{\omega t}$. The linearized
approximation gives a divergent response (at long times) but the nonlinear
terms make the response finite. We address the nonlinearity-induced finiteness
in two ways by separately treating the short and long time scales. At long
times, we use the traditional perturbative techniques to extract two drive
dependent behaviours - one, the amplitude of oscillation scales as
$(H/\omega^{2})^{1/3}$ and, two, the time period of the slow mode varies as
$(H/\omega^{2})^{-2/3}$. For the early time behaviour, on the other hand, we
devise an alternate perturbative expansion where the successive terms get
larger with the order of evaluation but have alternating signs. The alternating
signs (phase differences) between these terms leads to adestructive
interference like effect. A careful consideration of this destructive
interference like effect between successive terms leads to a finite response
which describes the initial behaviour of the amplitude of the response
reasonably correctly. We further note that for larger drive values, the system
seems to undergo a first order transitional behaviour with a sudden jump in the
largest Lyapunov exponent.
