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၀ရ R - + vo(t) v(t) C Figure Q7 (a) 07 (a) A second order RLC...
၀ရ R - + vo(t) v(t) C Figure Q7 (a) 07 (a) A second order RLC circuit is given in Figure Q7 (a). Determine; (i) the time domain input-output relationship of the RLC circuit, (3 marks) (ii) the frequency response, H(W) of the circuit, (3 marks) (iii) the impulse response, h(t) given that R = 12, C = 1 F and L = 2 H. (4 marks) (b) An input vi(t) = e-ztu(t) is passed as the input to the...
HI, PLEASE ANSWER ALL PARTS AND PLEASE SHOW ALL WORKINGS STEP BY STEP. THANK YOU. a)...
HI, PLEASE ANSWER ALL PARTS AND PLEASE SHOW ALL WORKINGS STEP BY STEP. THANK YOU. a) Show from first principles that the Laplace transform of the function (0)=1, a 20 is f(3) = Make a note of any conditions imposed on the transform variable "s" to ensure the transform exists. (8 Marks) b) Find, using the appropriate theorem, the Laplace transform of a function f(t): f(t) = e-3t.sin(4t) OR Find the inverse Laplace transform of the following: ses f(s) =...
4- (10 points) In the following circuit, use Laplace Transform to find Vo(s). Consider the following...
4- (10 points) In the following circuit, use Laplace Transform to find Vo(s). Consider the following initial conditions in the inductor and capacitor: V.(0) - IV, 10) - 1A Follow the following steps in your solution. a) Draw the equivalent circuit in the Laplace Domain taking into account the initial conditions, and using the parallel model (see below) b) Use CDR or VDR to find Vo(s). c) Leave your answer in the Laplace Domain simplifying Vo(s) as a ratio of...
EET315 Netwi -2019 Winter 4. Using Laplace Transform to calculate Vo(t) for the following circuit, and power supply V=10 volts; all the rest components (capacitor, resistor, inductor) are represe...
EET315 Netwi -2019 Winter 4. Using Laplace Transform to calculate Vo(t) for the following circuit, and power supply V=10 volts; all the rest components (capacitor, resistor, inductor) are represented by C, R and L T-O Volt)
EET315 Netwi -2019 Winter 4. Using Laplace Transform to calculate Vo(t) for the following circuit, and power supply V=10 volts; all the rest components (capacitor, resistor, inductor) are represented by C, R and L T-O Volt)
10 sin 2t if 0 <t< 4. (a) Let r(t) if t > T Show that...
10 sin 2t if 0 <t< 4. (a) Let r(t) if t > T Show that the Laplace transform of r(t) is L(r) 20(1 - e - e-78) 32 + 4 (b) Find the inverse Laplace transform of each of the following functions: s – 3 S2 + 2s + 2 20 ii. (52 + 4)(52 + 25 + 2) 20e-S ini. (s2 + 4)(52 + 25 + 2) (c) Solve the following initial value problem for a damped mass-spring...
3. Natural response, for ? > 0 of a series R-L-C circuit has R = 1...
3. Natural response, for ? > 0 of a series R-L-C circuit has R = 1 Ω , L = 1 H and C = 1 F. The initial capacitor voltage is 4 V, and initial inductor current is zero. The series current is i. (i) Draw the time domain circuit. (ii) Draw the Laplace transform domain circuit. (iii) From (ii), determine Io =Io (s) (iv) From (iii), determine ?? = ??(?) for t > 0
2-If X1(z)Find the Z-Transform of X2[x]-X, ln +3]u[n] Find theZ-Transform of X211 ( I-hind the ...
2-If X1(z)Find the Z-Transform of X2[x]-X, ln +3]u[n] Find theZ-Transform of X211 ( I-hind the Inverse Z-transform of given function. a) R(Z) =- (1-e") (-(z-e-ar) 3 +282+8-1 b) F (Z) = (2-2)2(2+2) Find the Z-Transform of X2 [x] = X1 [n + 3] u [n] 3- Solve the difference equation 3 4 With initial conditions y-1] 1 and yl-2] 3 4- Let the step response of a linear, time-invariant, causal system be 72 3) ulnl 15 3 a) Find the...
4. (20 points) An ideal analog integrator is described by the system function: H(s) 1) Design...
4. (20 points) An ideal analog integrator is described by the system function: H(s) 1) Design a discrete-time "integrator" using the bilinear transformation with Ts 2 sec. t is the difference equation relating xin) to yin) thint: divide top and bottom of H(Z) by ) 3) Determine the unit sample (impulse) response of the digital fite. 4) Assuming a sampling frequency of 0.5 Hz, use the impulse invariance method to find an approximation for Hz). Hint: Inverse Laplace Transform of...
(1 point) In this exercise we will use the Laplace transform to solve the following initial...
(1 point) In this exercise we will use the Laplace transform to solve the following initial value problem: y" + 16 16, = { 10, 0<t<1 1<t , y(0) = 3, y'(0 = 4 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)), find the equation obtained by taking the Laplace transform of the initial value problem (2) Next solve for Y = (3) Finally apply the inverse Laplace transform to find y(t) y(t) =...
8 H 2 Q iL Vs (t 22 1. vs (t) 2 V; this is a...
8 H 2 Q iL Vs (t 22 1. vs (t) 2 V; this is a dc source. Solve using a simple circuit analysis method 2. Us (t) 2u (t) V; solve by writing and solving the differential equation for the circuit, as in Ch. 8. You = = 0 for t0. can assume that ir 2u (t) V; solve using the Thévenin method, as in Ch. 8. You can assume that i, = 0 for t< 0. 3. vg...
၀ရ R - + vo(t) v(t) C Figure Q7 (a) 07 (a) A second order RLC circuit is given in Figure Q7 (a). Determine; (i) the time domain input-output relationship of the RLC circuit, (3 marks) (ii) the frequency response, H(W) of the circuit, (3 marks) (iii) the impulse response, h(t) given that R = 12, C = 1 F and L = 2 H. (4 marks) (b) An input vi(t) = e-ztu(t) is passed as the input to the...
HI, PLEASE ANSWER ALL PARTS AND PLEASE SHOW ALL WORKINGS STEP BY STEP. THANK YOU. a) Show from first principles that the Laplace transform of the function (0)=1, a 20 is f(3) = Make a note of any conditions imposed on the transform variable "s" to ensure the transform exists. (8 Marks) b) Find, using the appropriate theorem, the Laplace transform of a function f(t): f(t) = e-3t.sin(4t) OR Find the inverse Laplace transform of the following: ses f(s) =...
4- (10 points) In the following circuit, use Laplace Transform to find Vo(s). Consider the following initial conditions in the inductor and capacitor: V.(0) - IV, 10) - 1A Follow the following steps in your solution. a) Draw the equivalent circuit in the Laplace Domain taking into account the initial conditions, and using the parallel model (see below) b) Use CDR or VDR to find Vo(s). c) Leave your answer in the Laplace Domain simplifying Vo(s) as a ratio of...
EET315 Netwi -2019 Winter 4. Using Laplace Transform to calculate Vo(t) for the following circuit, and power supply V=10 volts; all the rest components (capacitor, resistor, inductor) are represented by C, R and L T-O Volt)
EET315 Netwi -2019 Winter 4. Using Laplace Transform to calculate Vo(t) for the following circuit, and power supply V=10 volts; all the rest components (capacitor, resistor, inductor) are represented by C, R and L T-O Volt)
10 sin 2t if 0 <t< 4. (a) Let r(t) if t > T Show that the Laplace transform of r(t) is L(r) 20(1 - e - e-78) 32 + 4 (b) Find the inverse Laplace transform of each of the following functions: s – 3 S2 + 2s + 2 20 ii. (52 + 4)(52 + 25 + 2) 20e-S ini. (s2 + 4)(52 + 25 + 2) (c) Solve the following initial value problem for a damped mass-spring...
2-If X1(z)Find the Z-Transform of X2[x]-X, ln +3]u[n] Find theZ-Transform of X211 ( I-hind the Inverse Z-transform of given function. a) R(Z) =- (1-e") (-(z-e-ar) 3 +282+8-1 b) F (Z) = (2-2)2(2+2) Find the Z-Transform of X2 [x] = X1 [n + 3] u [n] 3- Solve the difference equation 3 4 With initial conditions y-1] 1 and yl-2] 3 4- Let the step response of a linear, time-invariant, causal system be 72 3) ulnl 15 3 a) Find the...
4. (20 points) An ideal analog integrator is described by the system function: H(s) 1) Design a discrete-time "integrator" using the bilinear transformation with Ts 2 sec. t is the difference equation relating xin) to yin) thint: divide top and bottom of H(Z) by ) 3) Determine the unit sample (impulse) response of the digital fite. 4) Assuming a sampling frequency of 0.5 Hz, use the impulse invariance method to find an approximation for Hz). Hint: Inverse Laplace Transform of...
(1 point) In this exercise we will use the Laplace transform to solve the following initial value problem: y" + 16 16, = { 10, 0<t<1 1<t , y(0) = 3, y'(0 = 4 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)), find the equation obtained by taking the Laplace transform of the initial value problem (2) Next solve for Y = (3) Finally apply the inverse Laplace transform to find y(t) y(t) =...
8 H 2 Q iL Vs (t 22 1. vs (t) 2 V; this is a dc source. Solve using a simple circuit analysis method 2. Us (t) 2u (t) V; solve by writing and solving the differential equation for the circuit, as in Ch. 8. You = = 0 for t0. can assume that ir 2u (t) V; solve using the Thévenin method, as in Ch. 8. You can assume that i, = 0 for t< 0. 3. vg...
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