The input and output voltages, vlt) and vo(t), of a series rc network are related by the differential equation v (s) v, (s) (a) if v,(s) lvand v(s) , show that the transfer function, is given by scr+1 (b) if c-0.1μf, r-100 kω find, and plot the graph of the response, vo(t), when sid, volts t> 0 t < 0 (c) using the component values given in (b) find the response when the input is a unit step function, t (d) using the component values given in (b) use the convolution theorem to determine the response when y(σ3dela

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Fft review: linspace, fs, fftshift, nfft 1. generate one second of a cosine of w,-10hz sampled at f, = 100hz and assign it to x. define a tt as your time axis 2. take 64 points fft. 3. as you remember, the dft (which the fft implements) computes n samples of s2t where k-0,1,2, n -1. plot the magnitude of this 64-points fft at range 0 to 63, what do you think of this graph? 4â·to get the x-axis into a hz-frequency form, plot this 64-points fft between-50 to 50 (the 100hz sampling rate) and have n-points between them. 5. according to your figure, what frequency is this cosine wave at? 6. remember that the fft is evaluating from 0 to 2ď€. we are used to viewing graphs from-ď€ to ď€. therefore, you need to shift your graph. 7. now according to your shifted graph. what frequency is this at? 8. note that the spikes have long drop-offs? try a 1024-point dft. note that the peak is closer to 10 and the drop-off is quicker. although, now sidelobes are an issue

The mass of the sun is 1.99×1030kg and its distance to the earth is 1.50×1011m. what is the gravitational force of the sun on the earth?