Answer
$\phi = 1.82~rad$
Work Step by Step
$x = x_m cos(\omega t+\phi)$
$a = -x_m \omega^2 cos(\omega t+\phi)$
We can consider $t = 0$ to find $\phi$:
$a = -x_m \omega^2 cos(\omega t+\phi) = 0.25 x_m \omega^2$
$cos(0+\phi) = -0.25$
$cos(\phi) = -0.25$
$\phi = 1.82$ or $\phi = 4.46$
As $t$ increases from zero, the value of $a$ becomes more positive.
Thus the value of $cos(\omega t+\phi)$ becomes more negative.
Therefore, $\phi = 1.82~rad$
