#### transgalactic

##### Banned

this is the last part of a bigger question

if you i forgot to mention some data please tell

in the last part i got

[latex]\ddot{v_c}+2\dot{v_c}+2v_c=v_s(t)[/latex]

[latex]\dot{v_c(0)}=2[/latex]

[latex]v_c(0)=0[/latex]

i need to find out if the response for [latex]v_s(t)=u(t)+cos(t)[/latex]

equals the sum of [latex]v_c^u[/latex](the response for spet function) and [latex]v_c^cos[/latex] the response for cosine

i start by finding the response for cos(t)

[latex]v_c(t)->V_c(s)[/latex]

[latex]\dot{v_c}->sV_c(s)-v_c(0)[/latex]

[latex]\ddot{v_c}->s(sV_c(s)-v_c(0))-\dot{v_c(0)}[/latex]

[latex]s(sV_c(s)-v_c(0))-\dot{v_c(0)}+2sV_c(s)-v_c(0)+2V_c(s)=\frac{s}{s^2+1}[/latex]

[latex]

V_c(s)[s^2+2s+2]+2=\frac{s}{s^2+1}

[/latex]

so i get

[latex]

V_c(s)=\frac{s}{(s^2+2s+2)(s^2+1)}-\frac{2}{s^2+2s+2}

[/latex]

where [latex]\dot{v_c}=j\omega v_c[/latex]

so now i need to break the fractures into a simpler ones

but here its all complex and i dont know how to get

a simpler fractures and there foorier transformation

??

so this is where i got stuck

and i even didnt get closer to the main solution of the problem

??

if you i forgot to mention some data please tell

in the last part i got

[latex]\ddot{v_c}+2\dot{v_c}+2v_c=v_s(t)[/latex]

[latex]\dot{v_c(0)}=2[/latex]

[latex]v_c(0)=0[/latex]

i need to find out if the response for [latex]v_s(t)=u(t)+cos(t)[/latex]

equals the sum of [latex]v_c^u[/latex](the response for spet function) and [latex]v_c^cos[/latex] the response for cosine

i start by finding the response for cos(t)

[latex]v_c(t)->V_c(s)[/latex]

[latex]\dot{v_c}->sV_c(s)-v_c(0)[/latex]

[latex]\ddot{v_c}->s(sV_c(s)-v_c(0))-\dot{v_c(0)}[/latex]

[latex]s(sV_c(s)-v_c(0))-\dot{v_c(0)}+2sV_c(s)-v_c(0)+2V_c(s)=\frac{s}{s^2+1}[/latex]

[latex]

V_c(s)[s^2+2s+2]+2=\frac{s}{s^2+1}

[/latex]

so i get

[latex]

V_c(s)=\frac{s}{(s^2+2s+2)(s^2+1)}-\frac{2}{s^2+2s+2}

[/latex]

where [latex]\dot{v_c}=j\omega v_c[/latex]

so now i need to break the fractures into a simpler ones

but here its all complex and i dont know how to get

a simpler fractures and there foorier transformation

??

so this is where i got stuck

and i even didnt get closer to the main solution of the problem

??

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