- #1
eehelp150
- 237
- 0
Homework Statement
Find the forced response of VC(t)
Homework Equations
The Attempt at a Solution
W=1000
[tex]\frac{d^2V_C(t)}{dt^2}+\frac{R}{L}\frac{dV_C(t)}{dt}+\frac{V_C}{LC}=\frac{Vin}{LC}[/tex]
[tex]V_C(t)=Acos(1000t+\theta)[/tex]
Plug in Vc(t),R,L,C into equation 1
[tex]-10^6Acos(10^3t+\theta)-10^7Asin(10^3t+\theta)+10^7Acos(10^3t+\theta)=5*10^7cos(10^3t)[/tex]
Simplifying:
[tex](9*10^6)Acos(10^3t+\theta)-10^7Asin(10^3t+\theta)=5*10^7cos(10^3t)[/tex]
Trig ID
[tex]\sqrt{(9*10^6)^2+(10^7)^2}*Acos(10^3t+tan^-1(-\frac{9*10^6}{-10^7}))[/tex]
[tex]13.45*10^6Acos(10^3t+41.98°)[/tex]Is everything I've done so far correct? How do I find A?