Verify solution attempt, determine functional purpose of the system

Given the transfer function of a system:

0.0001163 s^2 + 0.07919 s + 1.612
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0.0001112 s^5 + 0.003739 s^4 + 0.05894 s^3 + 0.4631 s^2 + 0.7542 s + 1.612

Continuous-time transfer function.

The question asks me to determine the zero state response for the input f(t)=2sin(st)u(t), or:

2*sin(2*t)*heaviside(t)

My attempt at a solution:

take laplace transform of input signal

>>Xs=laplace(2*sin(2*t)*heaviside(t))
Xs 
=
4/(s^2 + 4)

multiply (s domain convolution) of X(s)H(s)=Y(s) to find output

>>Hs=(((10459*s)/10000 + 69018941/100000)*(s + 21))/((s + 151/10)*(s^2 + (1713*s)/100 + 222)*(s^2 + (351*s)/250 + 2163/500))
>>Ys=Xs*Hs
Ys=(4*((10459*s)/10000 + 69018941/100000)*(s + 21))/((s^2 + 4)*(s + 151/10)*(s^2 + (1713*s)/100 + 222)*(s^2 + (351*s)/250 + 2163/500))

then, determine time domain response y(t)=inverse laplace {Y(s)}

>>y=ilaplace(Ys)
y=(306072176000*exp(-(151*t)/10))/180254653253441 - (3449150772536287413*cos(2*t))/1128585148208010133 - (255714286302535934*sin(2*t))/1128585148208010133 + (6013013937808747678888*exp(-(351*t)/500)*(cos((958299^(1/2)*t)/500) + (31369531746646936379*958299^(1/2)*sin((958299^(1/2)*t)/500))/68867306190699219475221))/1966872147350180816343 - (580262941534015660265*exp(-(1713*t)/200)*(cos((5945631^(1/2)*t)/200) + (55603380510813243871*5945631^(1/2)*sin((5945631^(1/2)*t)/200))/65972451158539651288977))/217253335038154821736863

I have no way to verify this result, does this look reasonable?

Furthermore, the question asks to determine the functional purpose of the transfer function/system

I am unsure how to make this determination or even where is should start, any suggestions would be appreciated

[Jacques Hebert]

to determine the functional purpose of the system i have plotted the impulse and step response of the given transfer function, but i am unsure how to use this information to find the purpose/function of the system.

if my previous solution is also correct then the output of 2sin(2t)u(t)

is given the output of

again, i am unsure what function this information describes, any suggestions given would be appreciated.

edit:I wonder if possibly it can be considered the desired function is to increase small signal and decrease large signal to stabilize input? Is this something that can be formally expressed?