Answer
$t = 6.84\times 10^{-4}~s$
Work Step by Step
$E = E_{max}~sin~(2\pi~f~t)$
We can solve this equation for $t$:
$sin~(2\pi~f~t) = \frac{E}{E_{max}}$
$2\pi~f~t = arcsin(\frac{E}{E_{max}})$
$t = \frac{1}{2\pi~f}~arcsin(\frac{E}{E_{max}})$
We can find the least positive value of $t$:
$t = \frac{1}{2\pi~(100)}~arcsin(\frac{5}{12})$
$t = \frac{1}{2\pi~(100)}~(0.43)$
$t = 6.84\times 10^{-4}~s$
