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HW+_2+Solution

HW+_2+Solution

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1. Determine the average and RMS values for the function: y(t) = 5 + sin 6 π t over time periods (a) 0 – 0.1 seconds; (b) 0.4 – 0.5 seconds; and (c) 0 – 5 seconds. Comment on the nature and meaning of the results in terms of analysis of dynamics signals.
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2. For the following sine and cosine functions, determine the period, the frequency in hertz, and the circular frequency in radians / second. (a) sin 4 π t (b) 8 cosine 80t (c) 100 sin 10t The period, frequency in Hz, and circular frequency in rad/s are found from ω = 2 π f= 2 π /T 3. Find the Fourier series of the function shown in the following figure, assuming that the function has a period of 2 π . Plot an accurate graph of the first three partial sums of the resulting Fourier series. y(t)=0 for π≤t≤0 y(t)= - 1 for 0≤t≤π /2 y(t)=1 for π/2≤t≤π
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