Prelab 1. Using a hand calculation, find the Laplace transform of: 2 i, ft) 0.00
ID: 2249107 • Letter: P
Question
Prelab 1. Using a hand calculation, find the Laplace transform of: 2 i, ft) 0.0075-0.00034e-2.5rcos(22) + 0.087e-2.5'sin(22t)-0.0072e-8 2. Using a hand calculation, find the inverse Laplace transform of I H 2(s +3)s +5)(s7) s(s+8) s2+10s+100) 2 F(s) = i, (t) i,(0 3. Use a hand calculation to solve the circuit for the Laplace transforms of the FIGURE P2.41 loop currents shown in Figure P2.41.(Use mesh analysis in s-domain) Lab 1. Use MATLAB and the Symbolic Math Toolbox to Generate symbolically the time function ft) shown in Prelab 1. Generate symbolically F(s) shown in Prelab 2. Obtain your result symbolically in both factored and polynomial forms a. b. c. Find the Laplace transform of ft) shown in Prelab 1. d. Find the inverse Laplace transform of F(s) shown in Prelab 2. e. Generate an LTI transfer function for your symbolic representation of F(s) in Prelab 2 in both polynomial form and factored form. Start with the F(s) you generated symbolically. f. Solve for the Laplace transforms of the loop currents in Prelab 3.Explanation / Answer
(a)
>> syms t
>> f=0.0075-0.00034*exp(-2.5*t)*cos(22*t)+0.087*exp(-2.5*t)*sin(22*t)-0.0072*exp(-8*t)
f =
(87*sin(22*t)*exp(-(5*t)/2))/1000 - (17*cos(22*t)*exp(-(5*t)/2))/50000 - (9*exp(-8*t))/1250 + 3/400
(d)
>> laplace(f)
ans =
3/(400*s) - 9/(1250*(s + 8)) - (17*(s + 5/2))/(50000*((s + 5/2)^2 + 484)) + 957/(500*((s + 5/2)^2 + 484))
(b)
>>%factored form
>> syms s
>> F=(2*(s+3)*(s+5)*(s+7))/(s*(s+8)*(s^2+10*s+100))
F =
((2*s + 6)*(s + 5)*(s + 7))/(s*(s + 8)*(s^2 + 10*s + 100))
>>%polynomial form
>> n=2*conv([1 3],[1 5]);
>> n1=conv(n,[1 7]);
>> d=conv([1 0],[1 8]);
>> d1=conv(d,[1 10 100]);
>> sys=tf(n1,d1)
sys =
2 s^3 + 30 s^2 + 142 s + 210
------------------------------
s^4 + 18 s^3 + 180 s^2 + 800 s
Continuous-time transfer function.
(c)
>> ilaplace(F)
ans =
(5*exp(-8*t))/112 + (237*exp(-5*t)*(cos(5*3^(1/2)*t) + (3^(1/2)*sin(5*3^(1/2)*t))/9))/140 + 21/80