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Exam #1 Problem #1 Consider the system with the transfer function 30/(s2 + 8s+7) (5 pts) Is the system underdamped, overdamped, or critically damped? We need to find z. The value of z tells us whether the system is overdamped or critically damped or underdamped. Rearrange the polynomial into a more general form: t2s2 + 2tzs + 1:
So, t2 = 1/7, meaning t = 0.37796. 2tz = 8/7, so: This is greater than 1, so the system is overdamped.
(20 pts) If x(t) = e-6t, find an expression for y(t). Show all work. First invert x(t): So: Do partial fraction expansion: Use Heaviside expansion to find the constants. Multiply by s+7, let s = -7: Multiply by s+6, let s = -6: Multiply by s+1, let s = -1: So, Invert: |
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