diff --git a/_psets/11.md b/_psets/11.md
index 53432acac255d3d98ebadf91d37aa91a4dc8fbe8..7803f3851263b9f29bdfd05580b0e9b15c057492 100644
--- a/_psets/11.md
+++ b/_psets/11.md
@@ -47,6 +47,77 @@ Typical parameters for a quartz resonator are $$C_e = 5 \si{pF}$$, $$C_m = 20 \s
\si{mH}$$, $$R_m = 6 \si{\ohm}$$. Plot, and explain, the dependence of the reactance (imaginary part
of the impedance), resistance (real part), and the phase angle of the impedance on the frequency.
+The circuit in question is depicted in figure 14.4. There's a capacitance $$C_e$$ in parallel with
+a series RLC circuit ($$R_m$$, $$L_m$$, and $$C_m$$). To solve this it's helpful to know the complex
+impedances of the basic electrical components:
+
+$$
+\begin{align*}
+Z_C &= \frac{1}{i \omega C} \\
+Z_L &= i \omega L \\
+Z_R &= R
+\end{align*}
+$$
+
+Then we just combine these, using the sum for series connections, and the inverse of the sum of
+inverses for parallel connections. So the total impedance $$Z$$ is
+
+$$
+\begin{align*}
+\frac{1}{Z} &= \frac{1}{Z_{C_e}} + \frac{1}{Z_{C_m} + Z_{L_m} + Z_{R_m}} \\
+&= i \omega C_e + \frac{1}{1/(i \omega C_m) + i \omega L_m + R_m} \\
+&= i \omega C_e + \frac{\omega C_m}{-i + \omega C_m (R_m + i \omega L_m)} \\
+Z &= \frac{1}{i \omega C_e + \frac{\omega C_m}{\omega C_m (R_m + i \omega L_m) - i}}
+\end{align*}
+$$
+
+Let's see what this looks like with the given values plugged in. All the x axes are in radians per
+second.
+
+The resistance (real part) is very small except for a spike near $$\num{4e6} \si{rad/s}$$.
+
+
+
+Mathematica tells me the max occurs at
+
+$$
+\begin{align*}
+\omega_\text{max} &= \frac{1}{L_m} \sqrt{\frac{2 C_e L_m + 2 C_m L_m -C_e C_m R_m^2}{2 C_e C_m}} \\
+&\approx \num{4.09e6} \si{rad/s}
+\end{align*}
+$$
+
+But the first term in the numerator is a couple orders of magnitude larger than the others, so we
+can approximate $$\omega_\text{max}$$ by dropping them.
+
+$$
+\begin{align*}
+\omega_\text{max} &\approx \frac{1}{L_m} \sqrt{\frac{2 C_e L_m}{2 C_e C_m}} \\
+&= \frac{1}{\sqrt{C_m L_m}} \\
+&\approx \num{4.08e6} \si{rad/s}
+\end{align*}
+$$
+
+The reactance decreases without bound as $$\omega$$ approaches zero, and tends toward 0 as
+$$\omega$$ increases. It has a kink in about the same place the resistance has a spike.
+
+
+
+Finally the phase is almost always $$-\pi$$, except where it shoots just above one (radian), again
+near $$\omega = 1/\sqrt{C_m L_m}$$.
+
+
+
+Let's zoom in on those spikes.
+
+
+
+
+
+$$
+\begin{align*}
+\end{align*}
+$$
## (14.5)
diff --git a/_sass/main.scss b/_sass/main.scss
index 504e66300de0fda0793e34104310bce0dc6dc471..0dc99a8e1f09154553fa02853567d020a832cb2d 100644
--- a/_sass/main.scss
+++ b/_sass/main.scss
@@ -46,3 +46,7 @@ table, th, td {
th, td {
padding: 5px 10px;
}
+
+img {
+ width: 100%;
+}
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