A simple harmonic oscillator's velocity is given by

vy$($t$)=(0\mathrm{.}860$ m$/$s$)$sin$(10\mathrm{.}6$t $4\mathrm{.}75).$

Find the oscillator's position, velocity, and acceleration at each of the following times. $($Include the sign of the value in your answer.$)$

$($a$)$

t $=0$

position

m

velocity

$0\mathrm{.}853$ m$/$s

acceleration

m$/$s$2$

$($b$)$

t $=0\mathrm{.}500$ s

position

m

velocity

$0\mathrm{.}443$ m$/$s

acceleration

m$/$s$2$

$($c$)$

t $=2\mathrm{.}00$ s

position

m

velocity

m$/$s

acceleration

m