A mass m $=0\mathrm{.}400$ kg that is connected to a spring with spring constant k $=60\mathrm{.}0$ N$/$m is stretched $15\mathrm{.}0$ cm to the right of its equilibrium position. At time t $=0,$ the mass is released from rest and subsequently undergoes simple harmonic motion.

$($a$)$Write down an expression for x$($t$),$ the position of the mass as a function of time $($for t $0),$ using cos$.$ Let x $=0$ be the equilibrium position of the mass and let x $>0$ be to the right.

$($b$)$Write down an expression for x$($t$)$ using sin$.$