Problem 4 (10 Points) Consider a system described by ☺ + 2y – 3y = 1 – u. (i) Find the transfer function of the system. (ii) Find a state space equation of the system.
1) A causal discrete-time system is described by the difference equation, y(n) = x(n)+3x(n-1)+ 2x(n-4) a) What is the transfer function of the system? b) Sketch the impulse response of the system
2. (20 pts) Solve the following ODE: 3. (30 pts) Solve the following (ODE. y"2y'2y = 2x
5. Solve the linear, constant coefficient ODE y" – 3y' + 2y = 0; y(0) = 0, y'(0) = 1. 6. Solve the IVP with Cauchy-Euler ODE x2y" - 4xy' + 6y = 0; y(1) = 2, y'(1) = 0. 7. Given that y = Ge3x + cze-5x is a solution of the homogeneous equation, use the Method of Undetermined Coefficients to find the general solution of the non-homogeneous ODE " + 2y' - 15y = 3x 8. A 2...
Consider the ODE: Y'" + y' + 2y + 3y = 0. If yı (t) and y2 (t) are two linearly independent solutions to above ODE, then all solutions to it may be written as y(t) = C1 yı(t) + C2 y2(t) for an appropriate choice of the constants C1 and C2 True O False
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 ....
Consider the linear system given by the following differential equation y(4) + 3y(3) + 2y + 3y + 2y = ů – u where u = r(t) is the input and y is the output. Do not use MATLAB! a) Find the transfer function of the system (assume zero initial conditions)? b) Is this system stable? Show your work to justify your claim. Note: y(4) is the fourth derivative of y. Hint: Use the Routh-Hurwitz stability criterion! c) Write the...
Let the LTI system be described by 3y' (t) + y(t) = 2x' (t) Find the output of this system y(t)= x(t)- hlt) for xt)= 3e 'ult).
For a system whose dynamics are expressed by the differential equation: 2° + 2y + 3y = 3u By selecting the sampling time 0.1 second and using the zero- order holder (ZOH), obtain the discrete time transfer function of the system: G (z) = Y (2) / U (Z).
For a system with the difference equation: y[n] = -2y[n-1] + x[n] + 2x[n-2], find a.The impulse response b.The step response