Using (13) sketch or graph a figure (similar to Fig. 291 in Sec. 12.3) of the deflection u(x, t) of a vibrating string(length L = 1, ends fixed, c =

1) starting with initial velocity 0 and initial deflection (k small, say, k = 0.01). \text { 7. } f(x)=k \sin 2 \pi x