How to use transfer functions to find signal

[geeee]

How do you find y(t) for the circuits given in the attached file when x1(t)=cos (2*pi*5000t) and x2(t)=cos (2*pi*5200t) ?

 

[pavel_adameyko]

Hi

Your circuit is linear so you can calculate output for x1 and x2 separately(i mean, output y1 for x1, x2 is grounded; y2 for x2, x1 grounded), then y=y1+y2. So for the first image y(t)=1/3(x1(t)+x2(t)). For the second, y(t)=1/5(x1(t)+x2(t)).
Reards.

 

[geeee]

thanks for the reply. so when we add two signals with different frequencies we just leave the equations as is ? like cos (at)+cos(bt) ? also, when the frequencies are the same like acos (at) and bcos (at) then what would be the case ?

 

[pavel_adameyko]

Hi
you just find transfer function from input to output for each signal, assuming all other = 0 (i. e. grounded). This transfer function may depend on signal frequency if you for example have frequency-dependent components in your network (but it's not your case). After doing all this, the overall output will be y(t)= TF1*x1(t)+TF2*y2(t)+.... The key point here is that for linear network you can calculate response for each input separately and then add them. Hope my explanation is clear.
Regards.