2. A system is described by the differential equation +ay (0) - bx (O). (a) Find

Question

2. A system is described by the differential equation +ay (0) - bx (O). (a) Find an equation for the magnitude of the frequency response function for this system. (b) In the differential equation, approximate the derivative as dy y(O) –(t-A) dt A and evalute at the time t=na. orm an equation (the difference equation) that predicts the current value of y from the prior value y and the current value of x. (c) Write a MATLAB program that solves the difference equation for a b 1, x (0) = cos 2ft) and finds the peak value of y(O) for values of f between O, and 1000 (use a logarith mic scale. Note that the value of a should change for each frequency. Each frequency should be sampled 20 times over a period, compare the result obtained with part a) of this prob lem. Use MATLAB plots to show your results. What happens if you sample 50 times or 100 times over a period?

Explanation / Answer

x(t) is actually We can use this to directly derive a formula for new values of x based on old values of x and it's derivative.

c)

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