A particle moves along the x axis. It is initially at the position $0\mathrm{.}340$ m$,$ moving with velocity $0\mathrm{.}220$ m$/$s and acceleration $-0\mathrm{.}300$ m$/$s$2.$ Suppose it moves with constant acceleration for $5\mathrm{.}30$ s$.$

$($a$)$ Find the position of the particle after this time.

$-2\mathrm{.}7075$

$-2\mathrm{.}71$

m

$($b$)$ Find its velocity at the end of this time interval.

$-1\mathrm{.}37$

$-1\mathrm{.}37$

m$/$s

We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it oscillates in simple harmonic motion for $5\mathrm{.}30$ s around the equilibrium position x $=0.$ Hint: the following problems are very sensitive to rounding, and you should keep all digits in your calculator.

$($c$)$ Find the angular frequency of the oscillation. Hint: in SHM$,$ a is proportional to x$.$

$0\mathrm{.}939$

$0\mathrm{.}939$

$/$s

$($d$)$ Find the amplitude of the oscillation. Hint: use conservation of energy.

$0\mathrm{.}4129$

$0\mathrm{.}413$

m

$($e$)$ Find its phase constant $0$ if cosine is used for the equation of motion. Hint: when taking the inverse of a trig function, there are always two angles but your calculator will tell you only one and you must decide which of the two angles you need.

$-0\mathrm{.}603$

$-0\mathrm{.}603$

rad

$($f$)$ Find its position after it oscillates for $5\mathrm{.}30$ s$.$

$-0\mathrm{.}137$

$-0\mathrm{.}137$

m

$($g$)$ Find its velocity at the end of this $5\mathrm{.}30$ s time interval.

$0\mathrm{.}365$

$0\mathrm{.}366$

m$/$s