Answer
$t = 6.73~ms$
Work Step by Step
$\mathscr{E} = \mathscr{E}_m~sin~(\omega_d t-\frac{\pi}{4})$
The emf reaches a maximum when $~~sin~(\omega_d t-\frac{\pi}{4}) = 1$
We can find $t$:
$sin~(\omega_d t-\frac{\pi}{4}) = 1$
$\omega_d t-\frac{\pi}{4} = \frac{\pi}{2}$
$\omega_d t = \frac{3\pi}{4}$
$t = \frac{3\pi}{4~\omega_d}$
$t = \frac{3\pi}{(4)~(350~rad/s)}$
$t = 6.73~ms$
