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A cantinuous aime sustem has hu folowing transfer fhunction and initial conditions and y(0)-1 the completest-sponse...
A system with input r(t) and output y(t) has transfer function G(s) = 10 (s +...
A system with input r(t) and output y(t) has transfer function G(s) = 10 (s + 1)(s + 2). Find y(t) for t ≥ 0 if the following inputs are applied (with zero initial conditions): (a) r(t) = u(t) (b) r(t) = e^ −t*u(t)
Problem 2: (40 pts) Part A: (20pts) A third-order system has an of Y(s)-L[y(t) corresponding to...
Problem 2: (40 pts) Part A: (20pts) A third-order system has an of Y(s)-L[y(t) corresponding to a unit step input u(t) is known to be input of u(t) and an output of y(t). The forced response portion 1 Ys) (3 +3s2+ 4s +5) = a) Determine the input-output differential equation for the system b) From your result in a), determine the transformed free response Yee (s) corresponding to initial conditions of: y(0)= y(0) = 0 and ý(0)-6 Part B (20pts)...
3) Consider the system depicted below xz Input: F. Output: x Assume that all initial conditions a...
3) Consider the system depicted below xz Input: F. Output: x Assume that all initial conditions are zero. a) Derive mathematical model of the system b Find unit step response c) Find the transfer function T(s) X2(s)/Fs) d) What is the final value of the output be. limx)-7) for F)- 4) Find the transfer function state space R(s) for each of the following sytems represented in a) 10 y-[1 0 0 b) 2 -3-8 3 -5 y-1 3 6 c)...
1.7-3 For a certain LTI system with the input f(t), the output y(t) and the two initial conditions (0) and 2(0), follow...
1.7-3 For a certain LTI system with the input f(t), the output y(t) and the two initial conditions (0) and 2(0), following observations were made 1(0) z2(0) eu(t) e(3+2)u(t) 2u(t) 0 0 (t) Determine v(t) when both the initial conditions are zero and the input f(t) is as shown in Fig. P1.7-3. Hint: There are three causes: the input and each of the two initial conditions. Because of linearity property, if a cause is increased by a factor k, the...
Using the classical method, solve if the initial conditions are , , and if the input...
Using the classical method, solve
if the initial conditions are
,
, and if the input if f(t)=u(t)
Do not use convolution.
(D? + 2D y(t) = (D+1) f(t) y(0) = 2 Y(0) = 1
NOTE 2: Initial conditions assumed to be 0 unless otherwise is stated 1) Consider the system depi...
NOTE 2: Initial conditions assumed to be 0 unless otherwise is stated 1) Consider the system depicted below Input: v, Output: vo Assume that c (0)2, v2 (0)0 a) b) c) d) Derive the mathematical model of the system using mesh current method Find unit impulse response Find unit step response Find the transfer function T(s)Vo (s)/V(s) 2) Consider the system depicted below 2,20.5 Input: v, Output: i Assume that i,(0) 1, vc(00 a) Derive the mathematical model of the...
2y"(t) + 3 y' (t) + y(t)=x"(t) +x'(t) - x(t), y(0) = -2, y'(0) = 0,...
2y"(t) + 3 y' (t) + y(t)=x"(t) +x'(t) - x(t), y(0) = -2, y'(0) = 0, u(t) is the step function. 1. Write an expression for Y(s); at first leave U(s) symbolic. Identify which part is the zero-state and which part is the zero-input frequency-domain solution. Identify which part is the transfer function and which part is the initial condition polynomial. You will need to use the following transform pairs or properties, noting that they apply to the input as...
Question # 1 : Find the transfer function represented by: ??(?) ?? + 5 ?(?) =...
Question # 1
: Find the transfer function represented by:
??(?) ?? + 5 ?(?) = 2 ?(?)
Then, find the response, c(t) to an input, r(t) = u(t) a unit
step, assuming zero initial conditions. Draw the block diagram and
write the transfer function inside it, and show the i/p and o/p
signals on the block diagram.
Question #1: Find the transfer function represented by: dc(t) + 5 c(t) = 2 r(t) dt Then, find the response, c(t) to...
UestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Fin...
uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described...
solve it with matlab 25.24 Given the initial conditions, y(0) = 1 and y'(0) = 1...
solve it with matlab
25.24 Given the initial conditions, y(0) = 1 and y'(0) = 1 and y'(0) = 0, solve the following initial-value problem from t = 0 to 4: dy + 4y = 0 dt² Obtain your solutions with (a) Euler's method and (b) the fourth- order RK method. In both cases, use a step size of 0.125. Plot both solutions on the same graph along with the exact solution y = cos 2t.
Problem 2: (40 pts) Part A: (20pts) A third-order system has an of Y(s)-L[y(t) corresponding to a unit step input u(t) is known to be input of u(t) and an output of y(t). The forced response portion 1 Ys) (3 +3s2+ 4s +5) = a) Determine the input-output differential equation for the system b) From your result in a), determine the transformed free response Yee (s) corresponding to initial conditions of: y(0)= y(0) = 0 and ý(0)-6 Part B (20pts)...
3) Consider the system depicted below xz Input: F. Output: x Assume that all initial conditions are zero. a) Derive mathematical model of the system b Find unit step response c) Find the transfer function T(s) X2(s)/Fs) d) What is the final value of the output be. limx)-7) for F)- 4) Find the transfer function state space R(s) for each of the following sytems represented in a) 10 y-[1 0 0 b) 2 -3-8 3 -5 y-1 3 6 c)...
1.7-3 For a certain LTI system with the input f(t), the output y(t) and the two initial conditions (0) and 2(0), following observations were made 1(0) z2(0) eu(t) e(3+2)u(t) 2u(t) 0 0 (t) Determine v(t) when both the initial conditions are zero and the input f(t) is as shown in Fig. P1.7-3. Hint: There are three causes: the input and each of the two initial conditions. Because of linearity property, if a cause is increased by a factor k, the...
Using the classical method, solve
if the initial conditions are
,
, and if the input if f(t)=u(t)
Do not use convolution.
(D? + 2D y(t) = (D+1) f(t) y(0) = 2 Y(0) = 1
NOTE 2: Initial conditions assumed to be 0 unless otherwise is stated 1) Consider the system depicted below Input: v, Output: vo Assume that c (0)2, v2 (0)0 a) b) c) d) Derive the mathematical model of the system using mesh current method Find unit impulse response Find unit step response Find the transfer function T(s)Vo (s)/V(s) 2) Consider the system depicted below 2,20.5 Input: v, Output: i Assume that i,(0) 1, vc(00 a) Derive the mathematical model of the...
2y"(t) + 3 y' (t) + y(t)=x"(t) +x'(t) - x(t), y(0) = -2, y'(0) = 0, u(t) is the step function. 1. Write an expression for Y(s); at first leave U(s) symbolic. Identify which part is the zero-state and which part is the zero-input frequency-domain solution. Identify which part is the transfer function and which part is the initial condition polynomial. You will need to use the following transform pairs or properties, noting that they apply to the input as...
Question # 1
: Find the transfer function represented by:
??(?) ?? + 5 ?(?) = 2 ?(?)
Then, find the response, c(t) to an input, r(t) = u(t) a unit
step, assuming zero initial conditions. Draw the block diagram and
write the transfer function inside it, and show the i/p and o/p
signals on the block diagram.
Question #1: Find the transfer function represented by: dc(t) + 5 c(t) = 2 r(t) dt Then, find the response, c(t) to...
uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described...
solve it with matlab
25.24 Given the initial conditions, y(0) = 1 and y'(0) = 1 and y'(0) = 0, solve the following initial-value problem from t = 0 to 4: dy + 4y = 0 dt² Obtain your solutions with (a) Euler's method and (b) the fourth- order RK method. In both cases, use a step size of 0.125. Plot both solutions on the same graph along with the exact solution y = cos 2t.
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