(c) (12 pts) A differential equation with specified causal input and initial conditions has Laplace transform...
In a continuous-time system, the laplace transform of the input X(s) and the output Y(s) are related by Y(s) = 2 (s+2)2 +10 a) If x(t) = u(t), find the zero-state response of the system, yzs(1). yzs() = b) Find the zero-input response of the system, yzi(t). Yzi(t) = c) Find the steady-state solution of the system, yss(t). Yss(t) =
(15 pts) Given the following differential equations with the initial condition y(0) = 1, determine (1) the zero-input response yzi(t), (2) the zero-state response yzs (t) and (3) the total response y(t) for the input x(t) = e-fu(t) by using Laplace Transform. (5 pts) x+6y(t) = x - x() (1) Yzi(t) = (2) yzs(t) = (3) y(t) = (5 pts) (5 pts) 2. (10 pts) Given the following differential equations, find the total response y(t) if y(0) = 1 for...
Consider the differential equation: 0)+ y(t)-x(), and use the unilateral Laplace Transform to solve the following problem. a. Determine the zero-state response of this system when the input current is x(t) = e-Hu(t). b. Determine the zero-input response of the system for t > 0-, given C. Determine the output of the circuit when the input current is x(t)- e-2tu(t) and the initial condition is the same as the one specified in part (b).
Problem 3: Insights into Differential Equations a. Consider the differential equation 습 +4 = f(t), where f(t) = e-u, 12 0. Please write the forms of the natural and forced solution for this differential equation. You DO NOT need to solve. (7 points) b. Again consider the differential equation f(t), where f(t) is an input and y(t) is the output (response) of interest. Please write the differential equation in state-space form. (10 points) c. The classical method for solving differential...
Question:
given a differential equation:
a. initial conditions for the plan and input are zero, derive
plan's transfer function in Laplace transform
b. using inverse Laplace transform, find the solution for the
differential equation for the plan (find function y(t)).
c. derive state-space model of the plan
d. Assume open-loop system with no controller added to the
plant, analyse the steady-state value of the system using final
value theorem and step input
e. Calculate value of the overshoot, rise time...
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)
(#9) use the laplace transform to solve to given differential
equation to the indicated initial conditions. where appropriate,
write 'f' in terms of unit step functions.
8. y-4y 0, y'(0) = 0 = 0. v'(0) = 4 9. y"-4y'+4y t'e2', y(0) 1
Consider a causal, linear and time-invariant system of continuous time, with an input-output relation that obeys the following linear differential equation: y(t) + 2y(t) = x(t), where x(t) and y(t) stand for the input and output signals of the system, respectively, and the dot symbol over a signal denotes its first-order derivative with respect to time t. Use the Laplace transform to compute the output y(t) of the system, given the initial condition y(0-) = V2 and the input signal...
differential equation with Solve the following given initial conditions using the Laplace transform. y" +Sy't by : 4 (t-1)-8(+-2) y 10) = -2 y 10) =5 and
Solve the following differential equation with given initial conditions using the Laplace transform. y" + 5y' + 6y = ut - 1) - 5(t - 2) with y(0) -2 and y'(0) = 5. 1 AB I