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1. Determine the average and RMS values for the function: y(t) = 5 + sin 6πt 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 4πt (b) 8 cosine 80t (c) 100 sin 10t The period, frequency in Hz, and circular frequency in rad/s are found from ω= 2πf= 2 π/T 3. Find the Fourier series of the function shown in the following figure, assuming that the function has a period of 2π. Plot an accurate graph of the first three partial sums of the resulting Fourier series. y(t)=0 for π≤t≤0y(t)= -1 for 0≤t≤π/2 y(t)=1 for π/2≤t≤π