RLC Energy Losses

A circuit contains a series combination of a switch, a $1 \, \Omega$ resistor, a $1 \, \text{mH}$ inductor, and a $1 \, \mu \text{F}$ capacitor. Prior to time $t = 0$ , the switch is open, the inductor is completely de-energized, and the capacitor is charged to $5 \, \text{V}$ . The switch then closes at $t = 0$ .

The circuit undergoes damped oscillation with time period $T$ . What fraction of the energy originally stored in the capacitor has been dissipated in the resistor as heat when $t = 5 \, T$ ? Give your answer as a number between $0$ and $1$ .

Note: Here, the notion of periodicity neglects the decaying envelope. Time periods are measured by counting waveform peaks of the same sign.