Steady periodic solutions

Take the forced vibrating string. Suppose that $L=1$, $a=1$. Suppose that the forcing function is a triangle wave, $\lvert t \rvert -\frac{\pi}{2}$ on $-\pi < t < \pi$ extended periodically. Find the particular solution.

The units are cgs (centimeters-grams-seconds). For $k=0.01$, $\omega = 1.991 \times {10}^{-7}$, $A_0 = 25$. Find the depth at which the summer is again the hottest point.