11. To alleviate the traffic congestion between two cities such as Paris and Seattle, engineers have proposed building a rail tunnel along a chord line connecting the cities. A train, unpropelled by any engine and starting from rest, would fall through the first half of the tunnel and then move up the second half. Assuming Earth is a uniform sphere and ignoring air drag and friction, find the city-to-city travel time. (Use 6.37 ×10⁶ m for earth radius and 5.98 × 10²⁴ kg for earth mass) (10分)

12. A High-Pass Filter. One application of L-R-C series circuits is to high-pass or lowpass filters, which filter out either the low- or high-frequency components of a signal. A highness filter is shown in Figure, where the output voltage is taken across the L-R combination. (a) Derive an expression for (Vout / Vs), the ratio of the output and source voltage amplitudes, as a function of the angular frequency ω of the source and R, L, and C parameters. (b) Show that when ω is small, this ratio is proportional to ω and thus is small, and (c) show that the ratio approaches unity in the limit of large frequency. [15分, find the reactance of L and C to construct the voltage and current]

相關申論題

相關試卷