Problem $3(20$ points$)$

A mass of $0\mathrm{.}9kg$ is attached to a horizontal

spring whose stiffness is $22\frac{N}{m}.$ Friction is

negligible. At $t=0s$ the spring has a stretch of

$0\mathrm{.}27m$ and the mass has a speed of $5\frac{m}{s}.$

a$)(5$ points$)$ Find the initial kinetic energy of the

mass.

$K_i=$

b$)(5$ points$)$ Find the initial energy stored in the

spring.

$U_i=$

c$)(5$ points$)$ What is the amplitude $($maximum

stretch$)$ of the oscillation?

$s_{\text{m}\text{a}\text{x}\text{.}}=,[m]$

d$)(5$ points$)$ What is the maximum speed

reached by the mass?

$v_{\text{m}\text{a}\text{x}\text{.}}=,[\frac{m}{s}]$ a$=9\mathrm{.}8$ m$/$s$^2$ if need $,$ need all steps and correct answer please to put thumbs up