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Consider a CTLTI system described by the following ordinary differential equation with constant coefficients: N M...
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider...
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
3. Consider the Linear Time-Invariant (LTI) system decribed by the following differential equation: dy +504 +...
3. Consider the Linear Time-Invariant (LTI) system decribed by the following differential equation: dy +504 + 4y = u(t) dt dt where y(t) is the output of the system and u(t) is the input. This is an Initial Value Problem (IVP) with initial conditions y(0) = 0, y = 0. Also by setting u(t) = (t) an input 8(t) is given to the system, where 8(t) is the unit impulse function. a. Write a function F(s) for a function f(t)...
Let a linear system with input x(t) and output y(t) be described by the differential equation...
Let a linear system with input x(t) and output y(t) be described
by the differential equation .
(a) Compute the simplest math function form of the impulse
response h(t) for this system. HINT: Remember that with zero
initial conditions, the following Laplace transform pairs hold:
Let the time-domain function p(t) be given by p(t) = g(3 − 0.5
t). (a) Compute the simplest piecewise math form for p(t).
(b) Plot p(t) over the range 0 ≤ t ≤ 10 ....
Q.4) [25 Marks] a) [15] Consider a CT LTI system described by the following differential equation...
Q.4) [25 Marks] a) [15] Consider a CT LTI system described by the following differential equation (assume zero initial conditions): dºy(t) _6dy(t) + 3 dy(t) = 2x(6) dt3-6 dt2 +8 dt = 2x(t) [5] Using Laplace transform and its properties determine the transfer function H(s) [5] Draw the pole-zero diagram of H(s) (5) Write down all possible Region-of-Convergence (ROC) for the H(s) (iii) [5] white b) (10) Determine the signal x(t) ( assume it to be right-sided signal) when the...
3.1 The relationship between the input x(t) and output y(t) of described by the indicated differential...
3.1 The relationship between the input x(t) and output y(t) of described by the indicated differential equation given below: a causal system is dx(t) dse)+540+6y(t) = x(t) +T Assuming that the initial conditions are zero and using the Laplace transform determine [5 Marks] 15 Marks the following: a- Transfer function H(s) of the system. b- Impulse response h(t) of the system. Y (s) X(s)
Consider a second order linear time invariant system represented by the following ordinary differential equation: 4....
Consider a second order linear time invariant system represented by the following ordinary differential equation: 4. dx(t) dt dt dt Y (s) X(s) a. Find the transfer function H(s) of the system. (5 Points)
need a step by step solution please Challenge problem for extra credit (10 points)-Prove using Laplace Transforms that, for a system described by a linear ordinary differential equation, sine in -...
need a step by step solution please
Challenge problem for extra credit (10 points)-Prove using Laplace Transforms that, for a system described by a linear ordinary differential equation, sine in -> sine out, and find the equation for the scaling
Challenge problem for extra credit (10 points)-Prove using Laplace Transforms that, for a system described by a linear ordinary differential equation, sine in -> sine out, and find the equation for the scaling
Assume a dynamic system is described by the following ordinary differential equation (ODE) 1. Assume a...
Assume a dynamic
system is described by the following ordinary differential equation
(ODE)
1. Assume a dynamic system is described by the following ordinary differential equation (ODE): y(4) + 9y(3) + 30ij + 429 + 20y F(t) = where y = (r' y /dt'.. (a) (10 %) Let F(t) = 1 for t 0, please solve the ODE analytically. (b) (10 %) Please give a brief comment to the evolution of the system. (c) (5 %) Please give a brief...
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.
2.6.1 Consider a causal continuous-time LTI system described by the differential equation u"(t) +...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
3. Consider the Linear Time-Invariant (LTI) system decribed by the following differential equation: dy +504 + 4y = u(t) dt dt where y(t) is the output of the system and u(t) is the input. This is an Initial Value Problem (IVP) with initial conditions y(0) = 0, y = 0. Also by setting u(t) = (t) an input 8(t) is given to the system, where 8(t) is the unit impulse function. a. Write a function F(s) for a function f(t)...
Let a linear system with input x(t) and output y(t) be described
by the differential equation .
(a) Compute the simplest math function form of the impulse
response h(t) for this system. HINT: Remember that with zero
initial conditions, the following Laplace transform pairs hold:
Let the time-domain function p(t) be given by p(t) = g(3 − 0.5
t). (a) Compute the simplest piecewise math form for p(t).
(b) Plot p(t) over the range 0 ≤ t ≤ 10 ....
Q.4) [25 Marks] a) [15] Consider a CT LTI system described by the following differential equation (assume zero initial conditions): dºy(t) _6dy(t) + 3 dy(t) = 2x(6) dt3-6 dt2 +8 dt = 2x(t) [5] Using Laplace transform and its properties determine the transfer function H(s) [5] Draw the pole-zero diagram of H(s) (5) Write down all possible Region-of-Convergence (ROC) for the H(s) (iii) [5] white b) (10) Determine the signal x(t) ( assume it to be right-sided signal) when the...
3.1 The relationship between the input x(t) and output y(t) of described by the indicated differential equation given below: a causal system is dx(t) dse)+540+6y(t) = x(t) +T Assuming that the initial conditions are zero and using the Laplace transform determine [5 Marks] 15 Marks the following: a- Transfer function H(s) of the system. b- Impulse response h(t) of the system. Y (s) X(s)
Consider a second order linear time invariant system represented by the following ordinary differential equation: 4. dx(t) dt dt dt Y (s) X(s) a. Find the transfer function H(s) of the system. (5 Points)
need a step by step solution please
Challenge problem for extra credit (10 points)-Prove using Laplace Transforms that, for a system described by a linear ordinary differential equation, sine in -> sine out, and find the equation for the scaling
Challenge problem for extra credit (10 points)-Prove using Laplace Transforms that, for a system described by a linear ordinary differential equation, sine in -> sine out, and find the equation for the scaling
Assume a dynamic
system is described by the following ordinary differential equation
(ODE)
1. Assume a dynamic system is described by the following ordinary differential equation (ODE): y(4) + 9y(3) + 30ij + 429 + 20y F(t) = where y = (r' y /dt'.. (a) (10 %) Let F(t) = 1 for t 0, please solve the ODE analytically. (b) (10 %) Please give a brief comment to the evolution of the system. (c) (5 %) Please give a brief...
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.
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
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