The modulating signal m(t) = 2 cos 4000πt + 4 cos 6000πt is multiplied by the carrier c(t) = 100 cos 2πfct, where fc = 50 kHz. Determine and sketch the spectrum of the DSB signal.

A5 foot by 5 foot box culvert is buried 6 feet beneath the surface of the ground. a crosssection of this very long culvert (into and out of the page) is illustrated below. assume that the soil in which the culvert is buried has the following properties: jt = 120 pcf, w = 12%, ko = 0.50, ka = 0.33, and kp = 3.00. calculate the total horizontal force per unit length of culvert (fh) felt on one of the vertical faces of the culvert.