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Problem 1: Referring to figure, compute the homogenous transforms [T 30° ZAYs Yc Xc 381 Problem...
Compute Laplace transforms of the following functions: (a) f1 = (1 + t) (b) f2 =...
Compute Laplace transforms of the following functions: (a) f1 = (1 + t) (b) f2 = eat sin(bt) 11, 0<t<1, (c) f3 = -1 1<t<2, | 2, t>2, Find the functions from their Laplace transforms: (a) Lyı] s(s + 1) (s +3) 2+s (b) L[42] = 52 + 2 s +5 (c) L[y3] = Solve the following initial value problems using the Laplace transform. Confirm each solution with a Matlab plot showing the function on the interval 0 <t<5. (a)...
Problem 7.3 r(t) has the Fourier transform Xjw Determine the Fourier transforms of the following signals....
Problem 7.3 r(t) has the Fourier transform Xjw Determine the Fourier transforms of the following signals. (a) Fal)-5r(3t -2) (b) r(t)(t 1)sin(2t) (c) elt)5) HINT: Find the value of r(t) first. (d) ralt) (t)cos(2mt
dan Multiplication by t. 8. Find the following Laplace transforms using the formula L[t"f(t)] = (-1)",...
dan Multiplication by t. 8. Find the following Laplace transforms using the formula L[t"f(t)] = (-1)", (a) [t3e-36] (b) C[(t + 2)2e'] (c) C[t(3 sin 2t - 2 cos 2t)] (d) L[tsin t] (e) C[t cosh 3t) (1) [(t-1)(t - 2) sin 3t] (g) [t3 cost] 9. Applying L[t"f(t)] = (-1)", , calculate (a) Sºte-3t sin t dt (b) Scºt?e-t cost dt recimento e contato Llegarsim 225 (-1)" IEC d'Fs) dsh
problem 7 Problem-4 [10 Points] Find the Laplace transforms of the functions in Figure. 2 Figure....
problem 7
Problem-4 [10 Points] Find the Laplace transforms of the functions in Figure. 2 Figure. 2: Triangular Function Problem-5 [10 Pointsl A system has the transfer function h(s) = (s1)(s +2) a) Find the impulse response of the system b) Determine the output y(t), given that the input is x(t) u(t) Problem-6 [10 Pointsl Use the Laplace transform to solve the differential equation +22+10v(t) 3 cos(2t) dt2 dt subject to v(0)-1, dv(O) Problem-7 [10 Points] Solve the integrodifferential equation...
5) Use the method of Laplace transforms to the solve the following boundary value problem IC: u(x...
5) Use the method of Laplace transforms to the solve the following boundary value problem IC: u(x, 0) 2 in the following way: a) Apply the Laplace transform in the variable of t to obtain the initial value problem b) Show that U =-+ cie'sz +cge-Vsz s the general solution to the above equation and solve for the constants c and c2 to obtain that c) By taking a power series about the origin and using the identities, sinh iz-...
Express the function below using window and step functions and compute its Laplace transform. 0, 0<t<3...
Express the function below using window and step functions and compute its Laplace transform. 0, 0<t<3 2, 3<t<5 g(t) = 6, 5<t<8 4, 8<t Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Express g(t) using window and step functions. Choose the correct answer below. O A. g(t) = 2ut - 3) + 6(t-5) + 4u(t-8) B. g(t) = 2113,5(t) + 6115,8(t) + 4u(t-8) O c. g(t) = 2113,5(t)...
Problem 7.1 (10 points) Express the unilateral z-transforms of the following functions as rational functions. Find...
Problem 7.1 (10 points) Express the unilateral z-transforms of the following functions as rational functions. Find also the ROC. You may use tables. (a) xl[n]-1-0.2)" (b) x2[n] (0.3)" +2(-5) -0.2n Problem 7.2 (10 points) Express the unilateral z-transforms of the following functions as rational functions. Find also the ROC. You may use tables. (a) xl[n] = 3e-j02" (b) x2[n]- 5cos(5n) (c) x3[n] = e-0.gn sin(0.7n) Problem 7.3 (10 points) The signals given are sampled every 0.3 s, beginning att-0. Find...
Chapter 16, Problem 16.025 Calculate vo(t) in the circuit shown in the figure below ifh(t) is...
Chapter 16, Problem 16.025 Calculate vo(t) in the circuit shown in the figure below ifh(t) is 200 cos(105t + 60°) mA, i2(t) is 100 sin( 105t + 90°) mA, and vs(t) = 10 sin(105t) V vcl!) 250 nF 36 Ohnvo() (a) Find the amplitude of vo(t) (b) Find the phase of vo(t) in degrees degrees Chapter 16, Problem 16.011 (Circuit Solution) Find Z in the network in the figure below 2? 1? 2? 2?
Problem 3. 0 Figure 2 Given: f(t) = { 2.5, -1.5 <=<= 1.5 f(t) = {...
Problem 3. 0 Figure 2 Given: f(t) = { 2.5, -1.5 <=<= 1.5 f(t) = { 0 otherwise See figure(2) above. A) Find the Fourier transform for f( (see figure 2) and sketch its waveform. B) Determine the values of the first three frequency terms (w1, W2, W3) where F(w) = 0. C) Given x(t) = 1.58(-0.8) edt Determine whether or not Fourier transform exists for x(t). If yes, find the Fourier transfe not explain why it does not. Problem...
5.5 Starting with the Fourier transform pair 2 sin(S2) X(t) = u(t + 1) – ut...
5.5 Starting with the Fourier transform pair 2 sin(S2) X(t) = u(t + 1) – ut - 1) = X(92) = S2 and using no integration, indicate the properties of the Fourier transform that will allow you to compute the Fourier transform of the following signals (do not find the Fourier transforms): (a) xz(t) = -u(t + 2) + 2u(t) – u(t – 2) (b) xz(t) = 2 sin(t)/t (C) X3 (t) = 2[u(t + 0.5) - ut - 0.5)]...
Compute Laplace transforms of the following functions: (a) f1 = (1 + t) (b) f2 = eat sin(bt) 11, 0<t<1, (c) f3 = -1 1<t<2, | 2, t>2, Find the functions from their Laplace transforms: (a) Lyı] s(s + 1) (s +3) 2+s (b) L[42] = 52 + 2 s +5 (c) L[y3] = Solve the following initial value problems using the Laplace transform. Confirm each solution with a Matlab plot showing the function on the interval 0 <t<5. (a)...
Problem 7.3 r(t) has the Fourier transform Xjw Determine the Fourier transforms of the following signals. (a) Fal)-5r(3t -2) (b) r(t)(t 1)sin(2t) (c) elt)5) HINT: Find the value of r(t) first. (d) ralt) (t)cos(2mt
dan Multiplication by t. 8. Find the following Laplace transforms using the formula L[t"f(t)] = (-1)", (a) [t3e-36] (b) C[(t + 2)2e'] (c) C[t(3 sin 2t - 2 cos 2t)] (d) L[tsin t] (e) C[t cosh 3t) (1) [(t-1)(t - 2) sin 3t] (g) [t3 cost] 9. Applying L[t"f(t)] = (-1)", , calculate (a) Sºte-3t sin t dt (b) Scºt?e-t cost dt recimento e contato Llegarsim 225 (-1)" IEC d'Fs) dsh
problem 7
Problem-4 [10 Points] Find the Laplace transforms of the functions in Figure. 2 Figure. 2: Triangular Function Problem-5 [10 Pointsl A system has the transfer function h(s) = (s1)(s +2) a) Find the impulse response of the system b) Determine the output y(t), given that the input is x(t) u(t) Problem-6 [10 Pointsl Use the Laplace transform to solve the differential equation +22+10v(t) 3 cos(2t) dt2 dt subject to v(0)-1, dv(O) Problem-7 [10 Points] Solve the integrodifferential equation...
5) Use the method of Laplace transforms to the solve the following boundary value problem IC: u(x, 0) 2 in the following way: a) Apply the Laplace transform in the variable of t to obtain the initial value problem b) Show that U =-+ cie'sz +cge-Vsz s the general solution to the above equation and solve for the constants c and c2 to obtain that c) By taking a power series about the origin and using the identities, sinh iz-...
Express the function below using window and step functions and compute its Laplace transform. 0, 0<t<3 2, 3<t<5 g(t) = 6, 5<t<8 4, 8<t Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Express g(t) using window and step functions. Choose the correct answer below. O A. g(t) = 2ut - 3) + 6(t-5) + 4u(t-8) B. g(t) = 2113,5(t) + 6115,8(t) + 4u(t-8) O c. g(t) = 2113,5(t)...
Problem 7.1 (10 points) Express the unilateral z-transforms of the following functions as rational functions. Find also the ROC. You may use tables. (a) xl[n]-1-0.2)" (b) x2[n] (0.3)" +2(-5) -0.2n Problem 7.2 (10 points) Express the unilateral z-transforms of the following functions as rational functions. Find also the ROC. You may use tables. (a) xl[n] = 3e-j02" (b) x2[n]- 5cos(5n) (c) x3[n] = e-0.gn sin(0.7n) Problem 7.3 (10 points) The signals given are sampled every 0.3 s, beginning att-0. Find...
Chapter 16, Problem 16.025 Calculate vo(t) in the circuit shown in the figure below ifh(t) is 200 cos(105t + 60°) mA, i2(t) is 100 sin( 105t + 90°) mA, and vs(t) = 10 sin(105t) V vcl!) 250 nF 36 Ohnvo() (a) Find the amplitude of vo(t) (b) Find the phase of vo(t) in degrees degrees Chapter 16, Problem 16.011 (Circuit Solution) Find Z in the network in the figure below 2? 1? 2? 2?
Problem 3. 0 Figure 2 Given: f(t) = { 2.5, -1.5 <=<= 1.5 f(t) = { 0 otherwise See figure(2) above. A) Find the Fourier transform for f( (see figure 2) and sketch its waveform. B) Determine the values of the first three frequency terms (w1, W2, W3) where F(w) = 0. C) Given x(t) = 1.58(-0.8) edt Determine whether or not Fourier transform exists for x(t). If yes, find the Fourier transfe not explain why it does not. Problem...
5.5 Starting with the Fourier transform pair 2 sin(S2) X(t) = u(t + 1) – ut - 1) = X(92) = S2 and using no integration, indicate the properties of the Fourier transform that will allow you to compute the Fourier transform of the following signals (do not find the Fourier transforms): (a) xz(t) = -u(t + 2) + 2u(t) – u(t – 2) (b) xz(t) = 2 sin(t)/t (C) X3 (t) = 2[u(t + 0.5) - ut - 0.5)]...
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