Note;
If the equation produces two distinct complex roots, m1 and m2
in polar form
m1=r ∠θ and
m2 =r ∠(−θ)
Then
xn = rn ( c1 cos(nθ) + c2 sin(nθ) )
Is the solution
Solve number 2 please Homework! This example illustrates how to proceed in the case of a...
Please solve using the general
solution method. Do not use Z-Transforms.
3.34. Consider the second-order homogeneous difference equation with initial conditions yl-1] pi and yl-2 P2. The coefficients a and a2 of the difference equation and the initial values p? and p2 are all real-valued, and will be left as parameters. a. Let z1 and 22 be the roots of the characteristic polynomial. On paper, solve the homogeneous difference equation for the three possibilities for the roots: 1. The roots...
This is a differential equation
result of 5. Physical spring-mass systems almost always have some damping friction, air resistance, or a physical damper, calleda dashpot Because damping is primarily a friction force, we assume it is proportional to the velocity of the mass and acts in the opposite direction. So the damping force is given by -bx' for some constant b>0.Again applying Newton's second law, the differential equation becomes mx" +bx'+kc = 0 .(1) as a Determine the auxiliary equation...
A quadratic equation is generally represented as, ax^2 + bx + c The root(s) of the above quadratic equation is computed using the following formula, root1 = (-b + sqrt(D))/ 2a root2 = (-b - sqrt(D))/2a Where D is the discriminant of the quadratic equation and is computed as, D = b^2 - 4ac Given the value of D, the roots of a quadratic equation can be categorized as follows, D > 0 : Two distinct real roots D =...
(1 point) Mark all of the possibilities that can arise when solving a quadratic equation as in the method of solving order 2 Cauchy-Euler equations. е A. One repeated real root. B. Two distinct real roots. C. No roots D. One complex root. E. Two complex roots. F. One real root and one complex root. G. None of the above (1 point) To find , and u, we would need to integrate which of the following? Mark all that apply....
1) Using Matlab, find all real and complex roots of the following polynomial equation: (x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)=8 2) Using Matlab, find the root for the following system of equations. Both x and y are positive. a: (x^2)cos(y)=1 b: e^(-4x)+1
Please solve part b and c and d !!
Consider the closed loop system shown in Figure 4. The root locus of that system is shown in Figure 5 (s+40s+8) R(s) Y(s) Figure 4 System block diagram of Problem 4 a) On the root locus plot, sketch the region of possible roots of the dominant closed-loop poles such that the system response to a unit step has the following time domain specifications. [5] i. Damping ratio, 20.76 ii. Natural frequency,....
solve these 3 problems please the equation for number
2 is (X1-X)^2 + (Y1-Y2)^2 + (Z1-Z2)^2 = (T1-T2)^2 C^2
260.g68) and (2,20.0000, 246-412s 1. At time 341.980us you receive the following signals: (1, -13.5000, Convert the locations in miles to locations in feet and the times in microseconds to nanoseconds. The speed of the radio signal is the speed of light. c, which happens to be 299,792.458 m/s exactly. For our purposes take the speed of light to be exactly...
Question B3 (10 marks) Solve the following homogeneous system of first order ODE dai di da dt x,(0)=2. Makesures ou usethe initial with the initial conditions (0):0 0)=1, is in the following form Hint: It is given that one of the solutions of the above system Useful formulas Case 1: A only have distinct roots for λ General solution is ,n) are the coresponding eigenvectors where K, (where i = 1,2, Case 2: For a system of n equations, the...
This assignment assesses the material covered in Modules 6-10. Write full and complete so- lutions, using full sentences where appropriate. Explain all row operations when computing an RREF. Answer the questions asked. Questions 1-5 are worth 20 points each. The bonus question is worth 10 points (but points on this assignment are capped at 100). Recommended Deadline: April 24th Final Deadline: May 1st. 1. Compute the inverse of the matrix A = 1 3 1 4 -1 1 2 0...
these are useful formjlas to solve this problem
please show all work! thank you
2.) Design compensator for zero steady-state error with 10% overshoot and 0.4s of Peak time for the open loop transfer function G specified below. Sketch the comparison between uncompensated and compensated responses. Also compare their root locus. Clearly mention the improvements achieved after compensation. (50 points = 10 pts for analyzing uncompensated system+5 pts for identifying controller type+25 pts for controller design+5 pts for response comparison+5...