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Question 1 Consider the system equation below, with ao-7, a1-1, bo-7, A-8, and w-7. a1ý+aoV-boF(t...
A linear, time-invariant system is modeled by the ordinary differential equation y(t) + 7y(t) = 14f(t) Let f(t) = e^-t cos(2t)u(t) and y(0-) = -1. (a) Find the transfer function of the system and place your answer in the standard form H(s) = bms^m + bm-1s^m-1 + ... + b1s + bo / s^n + an-1s^n-1 + ... + a1s + a0 (b) Determine the output of the system as Y(s) = Yzs(s) + Yzi(s) and place both the zero...
Consider the general sinusoidal function y(t)-Asin (wt + φ). Part a If A-1 and y(0)-1, what is φ? (Please state as a decimal answer, eg. 0.1 π-meaning add the zero in front) Enter answer here 0 of 6 attempts used CHECK ANSWER Part b If A-1 and y(0)-0.5, what is φ? Select the correct answer O 30 π Part c If y(t) describes the position with time, what is the proper formula for velocity with time? (Recall velocity is related...
QUESTION 28 3 points Save The Siter coefficients of a second-order digital IR filter are: ao-1,a1-2, a2-2, bo-1. b1-1/2, b2 1/8. (a's are numerator coetficients and b's are the denominator coefficients). Determine the value of the impulse response N4? QUESTION 29 6 points Save Answer An image is to be sampled with a signal-to-quantisation ratio of at least 55 dB. The image samples are non-negative. The image sample values fall within the range from 0 to 1. How many bits...
Consider a linear, time-invariant system with an input given by X(T) = A, sin(Wit) where w, is a specific frequency. The system has a frequency response given by the amplitude ratio (magnitude ratio) as a function of the frequency, Mw), and the phase difference as a function of frequency, °W). Write an expression for the corresponding output in terms of the input amplitude, A1, the input frequency, W1, the amplitude ratio, and the phase difference.
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced) response of the system to the following everlasting signals: (a) ft) 1, (b) ftet, (c) f(t) = 100cos(2t- 60°) Using the classical method, solve 2.5-1 (D +7D+12) ye) (D+ 2)f(¢} (0*)= 0, s(0+ ) = 1, and if the input f(t) is if the initial conditions are 8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced) response...
Problem 1 Let's consider an LTI system with intput and output relatex through the equation y(t) - --- (T 2) dr a) Find the impulse response h(t) for the given system (1). b) Is this system cansal or not? c) Determine the output of the system when the input x(t) is as shown below. Problem 2 Evaluate the following convolution where (t) and y(t) are plotted helow z(t) = z(t) * y(t) Hint. Expr the signals as a linear combination...
Question 4 Xi →ろ sin at it m2, PM Consider the system shown in figure where m is subjected to F Sin(w t). Calculate the system response when m1 m2 and Kt k2- k Question 4 Xi →ろ sin at it m2, PM Consider the system shown in figure where m is subjected to F Sin(w t). Calculate the system response when m1 m2 and Kt k2- k
3. Consider a system with the following state equation h(t)] [0 0 21 [X1(t) [x1(t) y(t) [0.1 0 0.1x2(t) X3(t) The unit step response is required to have a settling time of less than 2 seconds and a percent overshoot of less than 5%. In addition a zero steady-state error is needed. The goal is to design the state feedback control law in the form of u(t) Kx(t) + Gr(t) (a) Find the desired regon of the S-plane for two...
Structural Dynamics (12 points) For the system shown below, 1. Determine A) The equation of motion. B) The maximum steady state force in the damper. C) The maximum steady state absolute acceleration. D) The maximum steady state force in the spring. Given: x(t)-2" sin(3.2t) W= 5000 lbs. K 1,863.4 lb/in C- 5 lb-s/in Ct) (12 points) For the system shown below, 1. Determine A) The equation of motion. B) The maximum steady state force in the damper. C) The maximum...