Chapter 6, Problem 29P

Two voltages ${\nu }_1\left(t\right)=10\sqrt{2}\sin \left(500\pi t-\frac{3\pi }{4}\right)\text{V}$ and ${\nu }_2\left(t\right)=5\sin \left(500\pi t\right)\text{V}$ are applied to the Op-Amp circuit shown in Fig.P6.29.

(a) Write down the amplitude, frequency (in Hz), period (in seconds), phase shift (in radians), and time shift in seconds) of the voltage ${\nu }_1\left(t\right)$.

(b) Plot one cycle of the voltage ${\nu }_1\left(t\right)$, and indicate the earliest time after $t=0$ when the voltage is $10\sqrt{2}\text{V}$.

(c) The output voltage ${\nu }_0\left(t\right)$ is given by ${\nu }_0\left(t\right)={\nu }_1\left(t\right)+{\nu }_2\left(t\right)$, write ${\nu }_0\left(t\right)$ in the form ${\nu }_0\left(t\right)=M\sin \left(500\pi t+\theta \right)$ ; in other words, find M and $\theta$.