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Name: I.D. #: HWC2 1) Determine the forced response for the following system described by the...
Please show all the steps, Thank you! Find yol(t), the zero-input component of the response for an LTIC system described by the following differential equation: (D2 + 6D +9)y(t) (3D+5)r(t) where the i...
Please show all the steps, Thank you!
Find yol(t), the zero-input component of the response for an LTIC system described by the following differential equation: (D2 + 6D +9)y(t) (3D+5)r(t) where the initial conditions are yo(0)-3)0(0) -7
Find yol(t), the zero-input component of the response for an LTIC system described by the following differential equation: (D2 + 6D +9)y(t) (3D+5)r(t) where the initial conditions are yo(0)-3)0(0) -7
Problem 3 A system is described by the following second-order linear differential equation d'y dz 5y(sin2t+...
Problem 3 A system is described by the following second-order linear differential equation d'y dz 5y(sin2t+ e-t)u(t) dt2 where y(0)y()0 Solve the differential equation using the Laplace Transform method.
Question 2 A linear time-invariant (LTI) system has its response described by the following second-order differential...
Question 2 A linear time-invariant (LTI) system has its response described by the following second-order differential equation: d'y) 3-10))-3*0)-6x0) dy_hi dx(t) where x() is the input function and y(t) is the output function. (a) Determine the transfer function H(a) of the system. (b) Determine the impulse response h(t) of the system.
8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced)...
8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced) response of the system to the following everlasting signals: (a) ft) 1, (b) ftet, (c) f(t) = 100cos(2t- 60°) Using the classical method, solve 2.5-1 (D +7D+12) ye) (D+ 2)f(¢} (0*)= 0, s(0+ ) = 1, and if the input f(t) is if the initial conditions are
8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced) response...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww +...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)
Q2. Consider the system described by the following differential equation x(t) Ax(t) where and x(0) -
Q2. Consider the system described by the following differential equation x(t) Ax(t) where and x(0) -
Q3. Let Grepresent a system described by the following differential equation: diye) + y(t) = dre)...
Q3. Let Grepresent a system described by the following differential equation: diye) + y(t) = dre) - 10) where x(1) is the input signal and y(t) is the output signal. a. (15 points) Determine the output yı(t) of G when the input is x below: 0 0 : otherwise b. (10 points) Consider a feedback loop that contains the system G, as shown below: Find a differential equation that relates w(l) to yo) when K = 10. Your differential equation...
Consider a mass-spring-damper system whose motion is described by the following system of differe...
Consider a mass-spring-damper system whose motion is described by the following system of differentiat equations [c1(f-k)+k,(f-х)-c2(x-9), f=f(t), y:' y(t) with x=x( t), where the function fit) is the input displacement function (known), while xit) and yt) are the two generalized coordinates (both unknown) of the mass-spring-damper systenm. 1. Identify the type of equations (e.g. H/NH, ODE/PDE, L/NL, order, type of coefficients, etc.J. 2. Express this system of differential equations in matrix form, assume f 0 and then determine its general...
3. For following input/output system relationships, determine the impulse response h(t). Clearly show all the steps...
3. For following input/output system relationships, determine the impulse response h(t). Clearly show all the steps arriving to your answer. p(-)x(1-)a L(2- r)x(1)dr-L*-1)x(1)dr (10 points) y(t) a. b. (10 points) y(t) -00 4. (10 points) An LTI system has the impulse response: h(t) = 4e-0.75(-1)[u(t + 4) - u(t - 10)]. this system Causal or Non-Causal? You must justify your answer. A correct answer with no justification worth only 4 points Is
3. For following input/output system relationships, determine the...
Spring mass damper system with forced response, the forced system given by the equation For damping...
Spring mass damper system with forced response, the forced system given by the equation For damping factor:E-0.1 ; mass; m-| kg: stiffness of spring; k-100 Nm; f-| 00 N; ω Zun; initial condition: x (0)-2 cms; r(0) = 0. fsincot Task Marks 1. Write down the reduced equation into 2first orderns Hand written equations differential equations 2. Rearrange equation (1) with the following generalized equation 250, x+osinor calculations 3. Calculate the value of c calculations Hand calculations 4. Using the...
Please show all the steps, Thank you!
Find yol(t), the zero-input component of the response for an LTIC system described by the following differential equation: (D2 + 6D +9)y(t) (3D+5)r(t) where the initial conditions are yo(0)-3)0(0) -7
Find yol(t), the zero-input component of the response for an LTIC system described by the following differential equation: (D2 + 6D +9)y(t) (3D+5)r(t) where the initial conditions are yo(0)-3)0(0) -7
Problem 3 A system is described by the following second-order linear differential equation d'y dz 5y(sin2t+ e-t)u(t) dt2 where y(0)y()0 Solve the differential equation using the Laplace Transform method.
Question 2 A linear time-invariant (LTI) system has its response described by the following second-order differential equation: d'y) 3-10))-3*0)-6x0) dy_hi dx(t) where x() is the input function and y(t) is the output function. (a) Determine the transfer function H(a) of the system. (b) Determine the impulse response h(t) of the system.
8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced) response of the system to the following everlasting signals: (a) ft) 1, (b) ftet, (c) f(t) = 100cos(2t- 60°) Using the classical method, solve 2.5-1 (D +7D+12) ye) (D+ 2)f(¢} (0*)= 0, s(0+ ) = 1, and if the input f(t) is if the initial conditions are
8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced) response...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)
Q2. Consider the system described by the following differential equation x(t) Ax(t) where and x(0) -
Q3. Let Grepresent a system described by the following differential equation: diye) + y(t) = dre) - 10) where x(1) is the input signal and y(t) is the output signal. a. (15 points) Determine the output yı(t) of G when the input is x below: 0 0 : otherwise b. (10 points) Consider a feedback loop that contains the system G, as shown below: Find a differential equation that relates w(l) to yo) when K = 10. Your differential equation...
Consider a mass-spring-damper system whose motion is described by the following system of differentiat equations [c1(f-k)+k,(f-х)-c2(x-9), f=f(t), y:' y(t) with x=x( t), where the function fit) is the input displacement function (known), while xit) and yt) are the two generalized coordinates (both unknown) of the mass-spring-damper systenm. 1. Identify the type of equations (e.g. H/NH, ODE/PDE, L/NL, order, type of coefficients, etc.J. 2. Express this system of differential equations in matrix form, assume f 0 and then determine its general...
3. For following input/output system relationships, determine the impulse response h(t). Clearly show all the steps arriving to your answer. p(-)x(1-)a L(2- r)x(1)dr-L*-1)x(1)dr (10 points) y(t) a. b. (10 points) y(t) -00 4. (10 points) An LTI system has the impulse response: h(t) = 4e-0.75(-1)[u(t + 4) - u(t - 10)]. this system Causal or Non-Causal? You must justify your answer. A correct answer with no justification worth only 4 points Is
3. For following input/output system relationships, determine the...
Spring mass damper system with forced response, the forced system given by the equation For damping factor:E-0.1 ; mass; m-| kg: stiffness of spring; k-100 Nm; f-| 00 N; ω Zun; initial condition: x (0)-2 cms; r(0) = 0. fsincot Task Marks 1. Write down the reduced equation into 2first orderns Hand written equations differential equations 2. Rearrange equation (1) with the following generalized equation 250, x+osinor calculations 3. Calculate the value of c calculations Hand calculations 4. Using the...
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