Consider this system equation y(t)=x(t)*cos(3t). where,x(t)=input. Using the superposition theorem, we can prove that the system is linear.
For input x1(t), the output is y1(t)=x1(t)*cos(3t). For input x2(t), the output is y1(t)=x2(t)*cos(3t).
For input [x1(t)+x2(t)], the output is y(t)=[x1(t)+x2(t)]*cos(3t) That is, y(t)=y1(t)+y2(t). Hence the system is linear
But I can't get the meaning of this. y(t) is linear with respect to x(t) means when we plot a graph of y(t) v/s x(t),I should get a straight line passing through origin.
But for the above case, its not straight line.
Please clarify this confusion....
Also ,if it is found to be linear, the system is linear for any x(t) or not? I mean if we take x(t)=t*u(t) or x(t)=t^2*u(t)...now is the system linear for both cases ??
Please explain Thanks in advance