A conducting coil, with current i$($t$)=5\mathrm{.}40$e$0\mathrm{.}0250$t sin$(120$t$),$ with i in amperes and t in seconds, is placed next to a second coil, end to end. At t $=0\mathrm{.}840$ s$,$ a lab tech measures the emf across the second coil, and the result is

$3\mathrm{.}90$ V$.$

What is the mutual inductance $($in mH$)$ of the coils?