An object in simple harmonic motion $($horizontal$)$ has a mass of $2\mathrm{.}7$ kg and is attached to a spring with $k=756\frac{N}{m}.$ When the object is $23$ cm from equilibrium, it is moving at $3\mathrm{.}7\frac{m}{s}.$ Determine the,

a$.$ Amplitude, in cm$.$ Ans. $32$ cm

b$.$ Period, in ms$.$ Ans. $375$ ms

c$.$ Maximum speed. Ans. $5\mathrm{.}33\frac{m}{s}$

d$.$ Total energy of the system. Ans. $38\mathrm{.}5$ J

e$.$ Functional form: $x(t)=$Acos$(t+),$ assuming the object starting from equilibrium moving in the $+x$ direction.

Ans. $x(t)=(32c^{\text{'}}n)cos([16\mathrm{.}7\frac{\text{r}\text{a}\text{d}}{(s)}]t-\frac{}{2})$

f$.$ Position and direction of motion at $t=618ms.$ Ans. $-25$ cm $,$ moving left $($in the negative direction$)$