thomps68 - Final Exam - Matthew Thompson

# thomps68 - Final Exam - Matthew Thompson - Matthew Thompson...

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Unformatted text preview: Matthew Thompson - thomps68 EECE 213 Final Exam In[91]:= ltr = LaplaceTransform @ f_ @ t_ D , t_, s_ D : > Symbol @ ToUpperCase @ SymbolName @ f [email protected] s D In[92]:= Protect @ ltr D In[93]:= Off @ Clear:: wrsym , Remove:: rmptc D Problem 1 Part a ¶ t HeavisideTheta @ t D- DiracDelta @ t D Part b Zc @ s_ D : = 1 c s Part c The y-axis of a Bode plot measures gain in decibels (dB) Part d In[58]:= T @ s_ D : = Tmax I s Α + 1 M n In[59]:= soln = Solve B T @ ü Ω c D T @- ü Ω c D == Tmax 2 , Α F Out[59]= :: Α fi - Ω c- 1 + 2 1 n > , : Α fi Ω c- 1 + 2 1 n >> In[60]:= Α Rule = Last @ soln D Out[60]= : Α fi Ω c- 1 + 2 1 n > In[68]:= Slope @ n_ D = ¶ s T @ s D . : Α fi Ω c- 1 + 2 1 n > Out[68]=-- 1 + 2 1 n n Tmax 1 +- 1 + 2 1 n s Ω c- 1- n Ω c Printed by Mathematica for Students In[66]:= Tmin @ n_ D = Simplify B T @ ü Ω min D T @- ü Ω min D . Α Rule, 8 Tmax ˛ Reals, Tmax > <F Out[66]= Tmax Ω c 2 + K- 1 + 2 1 n O Ω min 2 Ω c 2- n In[67]:= Slope @ n_ D = H Tmin- Tmax L H Ω min- Ω c L . : Tmin fi Tmax Ω c 2 + K- 1 + 2 1 n O Ω min 2 Ω c 2- n > Out[67]=- Tmax + Tmax Ω c 2 +- 1 + 2 1 n Ω min 2 Ω c 2- n-Ω c + Ω min Part e [Answer in Exam booklet] Problem 2 In[76]:= Clear @ "Global` * " D ; Remove @ "Global` * " D Part a In[77]:= F @ s_ D = LaplaceTransform A HeavisideTheta @ t D A H 2- Α t L ª-Α t , t, s E Out[77]= A- Α H s + Α L 2 + 2 s + Α Part b In[78]:= F @ s_ D = LaplaceTransform A HeavisideTheta @ t D I ¶ t I 10 ª- 20 t Sin @ 30 t DMM , t, s E Out[78]=- 6000 1300 + 40 s + s 2 + 300 H 20 + s L 1300 + s H 40 + s L In[72]:= % Together Simplify Out[72]= 300 s 1300 + 40 s + s 2 In[79]:= F @ s_ D : = 300 s 1300 + 40 s + s 2 Part c In[80]:= f @ t_ D = InverseLaplaceTransform B s H s + 2000 L H s + 6000 L , s, t F Together Out[80]=- 1 2 ª- 6000 t I- 3 + ª 4000 t M In[81]:= f @ t_ D : = - 1 2 ª- 6000 t I- 3 + ª 4000 t M 2 thomps68 - Final Exam - Matthew Thompson.nb Printed by Mathematica for Students Part d In[85]:= f @ t_ D = InverseLaplaceTransform B 10 I s 2 + 3 s + 3 M 4356 + 157 s 2 + s 4 , s, t F Out[85]= 1 187 H 66 Cos @ 6 t D- 66 Cos @ 11 t D- 121 Sin @ 6 t D + 236 Sin @ 11 t DL Problem 3 In[127]:= Clear @ "Global` * " D ; Remove @ "Global` * " D Part a In[119]:= iL @ D : = Part b In[125]:= vc @ D = J 1 c s N H L s L J 1 c s N + H L s L J 1 c s N H L s L J 1 c s N + H L s L + 2 R * H Va L Out[125]= L Va c I 1 c s + L s M 2 R +...
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thomps68 - Final Exam - Matthew Thompson - Matthew Thompson...

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