BME533 Final Exam Questions And Already Passed Answers.

BME533 Final Exam Questions And
Already Passed Answers.
Unit Impulse Response - Answer Q(D)y(t) = P(D)δ(t)



find zero-input response, use zero-state initial conditions (Dy(0⁺) = 1, y(0⁺) = 0) to find constant values



h(t) = [P(D)yₙ(t)]µ(t)



Zero-State Response - Answer Yzs(t) = x(t)*h(t)



Partial Fraction - Answer Make sure F(x) is a proper fraction before solving



First order system - Answer exponential trend



First-order system: Gain - Answer H(s) = k/(s-p), Re(p1,2) ≤0



First-order system: Steady-state value (t→∞) - Answer -k/p



First-order system: Decay constant - Answer t1/2 = ln(1/2)/p = -ln(2)/p



Transfer Function (H(s)) - Answer = P(s)/Q(s) --> X-terms/Y-terms

= k[(s-z1)(s-z2)...(s-zm)]/[(s-p1)(s-p2)...(s-pn)]



where z terms are zeros and p terms are poles



Second-order System: Gain - Answer H(s) = k/(s-p1)(s-p2) , Re(p1,2) ≤0

, Zero-state response of 2nd order system - Answer Y(s) = H(s)X(s)



if p1≠ p2: y(t) = (k/(p1-p2)p1p2)[(p1-p2) + p2e^(p1t) - p1e^(p2t)]u(t)



if p1=p2=p: y(t) = k/p²[1-e^(pt) + pte^(pt)]u(t)



Critically damped 2nd order system - Answer p1 and p2 are real and equal roots



S.S.: k/p

decay constant: p (e^pt, te^pt)



Over-damped 2nd order system - Answer p1 and p2 are real and distinct roots



S.S.: k/p1p2

decay constant: p1 p2 (e^p1t, e^p2t)



Underdamped 2nd order system - Answer p1 and p2 are complex and conjugate roots

p1,2 = σ ± jω



S.S.: k/p1p2

oscillation period: 2π/ω

decay constant: σ



Undamped 2nd order system - Answer p1 and p2 are imaginary and conjugate roots

p1,2 = jω



S.S.: k/p1p2

oscillation period: 2π/ω

decay constant: 0