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please help. Note: u(t) is unit-step function Consider the system with the differential equation: dyt) +...
Consider the following second-order ODE representing a spring-mass-damper system for zero initial conditions (forced response): where u is the Unit Step Function (of magnitude 1 a. Use MATLAB to obtain an analytical solution x() for the differential equation, using the Laplace Transforms approach (do not use DSOLVE). Obtain the analytical expression for ao. Also obtain a plot of x() (for a simulation of 14 seconds) b. Obtain the Transfer Function representation for the system. c. Use MATLAB to obtain the...
Find the zero-state response of the linear system with transfer function with an > 0 and 0 <くく1, when the input u(t) is the unit step, that is, u(t)-1(t), for 12 o, using both 1) the transfer function approach and 2) the convolution approach
Find the zero-state response of the linear system with transfer function with an > 0 and 0
Problem 3. Consider an LTIC system S. whose response to the unit-step function u(t) is as follows Slu(t)] Moreover, let the following input signal (t) go through the same LTIC system: r(t) 3 -2 1 Can you sketch/compute the output y(t) of the LTIC system S] to the input r(t) without using the impulse-response function h(t) of the system? Justify your answer!
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...
2) For a system with the transfer function H(s) =- (st100) c) find the unit impulse response of the system. d) if the input of the system is 3e u(t), what is the output of the system in the frequency domain if all initial conditions are zero. e) if the input of the system is 3e" 100u(t), what is the output of the system in the time domain if all initial conditions are zero. f) what is the frequency of...
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...
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...
Problem 5. Consider the dynamics of two mass mechanical system captured by d2xi(t) Middt?t2+k(x1(t)-x2(t)) = f(t) d'x2(t) dt2 + k(x2(t)-x where M, , M2, and k are constants. Suppose the input is () and the output is X2 (t), find the transfer function G(s) of the system. Note: Consider all zero initial conditions.
Matlab code for the following problems.
Consider the differential equation y(t) + 69(r) + 5y( Q3. t)u(t), where y(0) (0)0 and iu(t) is a unit step. Deter- mine the solution y(t) analytically and verify by co-plotting the analytic solution and the step response obtained with the step function. Consider the mechanical system depicted in Figure 4. The input is given by f(t), and the output is y(t). Determine the transfer function from f(t) to y(t) and, using an m-file, plot...
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)...