The magnetic flux through the loop shown in the accompanying figure varies with time according to $m = -ae^{-at} \sin(wt)$, where $a = 1 \times 10^{-3} \, \text{T} \cdot \text{m}^2$, $a = 3 \, \text{s}^{-1}$, and $w = 120 \, \text{T} \, \text{rad/s}$. What are the direction and magnitude of the current through the 5-ohm resistor at (a) $t = 0$; (b) $t = 2.17 \times 10^{-2} \, \text{s}$, and (c) $t = 3.00 \, \text{s}$?