H (8) Fig. Q1 Q2 [20 Marks] a) Consider the mechanical system shown in Fig. 22....
A Mechanical system is shown in Fig. 1.1. a) Obtain a set of simultaneous integro-differential equations, in terms of velocity, to represent the system, where k is spring Constant, m is the mass and b is damper. (Hint: draw two Free Body Diagrams and obtain two equations in terms of x1 and x2 only). X1 - Ft mi m2 M TTTTTTTTYYTTTTTTTTTYYTTTTTTT Fig 1.1 b) What components and energy source do you need to use in order to build an electric...
T duestions QUESTION 1: (20 marks) (a) A Mechatronic system uses a mechanical fioat valve system to sense and maintain the water level in a tank. The mechanical float vaive system is to be replaced to allow remote level indication ) State one type of sensor that could be used in the above (2 marks) Mechatronic system to sense the water level i) With the aid of a simple sketch, briefly describe the basic operation (4 marks) of the sensor...
Q2 (a) Consider the control system shown in Figure Q1 (a). Obtain the closed-loop transfer function of this system and by using MATLAB obtain the unit step response of this closed loop system - R(S) c(s) 36+1) (s + 1) Figure Q2 (a) (b) A sampler and a zero-order hold element were inserted into the system in Figure Q1(a) as shown in Figure Q1(b). Obtain the closed-loop pulse transfer function of this system and by using MATLAB or otherwise, obtain...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s)X2 (s)/F(s) (b) Does the system oscillate with a unit step input (f (t))? Explain the reason (c) Decide if the system(x2 (t)) is stable with a unit step input (f (t))? Explain the reason 1. 320) 8 kg 2 N/m 4N-s/m 2N-s/m Fig. 1 2. There are two suspensions for a car as shown in Fig. 2 (a) Find the equations of each...
1. (20 marks) This question is about the system of differential equations Y. dt=(k 1 (a) Consider the case k = 0. i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). ii. Write down the general solution. iii. Sketch a phase portrait for the system. (b) Now consider the case k3 In this case, the matrix has an eigenvalue 2+V/2 with eigenvector i. -1+iv2 and an eigenvalue 2 iv2 with eigenvector . Determine the type of equilibrium...
Question (20 marks) Consider a control system shown in Fig.2 has an open loop TF-G(s) H(s) 49 S(S+7) A-Prove that the gain margin=infinite db at infinite rad/sec. and the phase margin= 51.8 degrees at 5.5 rad/sec.? (4)
PHYS1047 a) Given a random variable x, with a continuous probability distribution function fx) 4 marks b) The life expectancy (in days) of a mechanical system has a probability density write down equations for the cumulative distribution C(x) and the survival distribution Px). State a relationship between them. function f(x)=1/x, for x21, and f(x)=0 for x <1. i Find the probability that the system lasts between 0 and I day.2 marks i) Find the probability that the system lasts between...
Question I : Consider the amplifier circuit shown below (p-150 for both transistors) (18 marks) +12V R4 1k8 R1 15k Q1 2N3904 C2+ 10μ R2 6V 4k7 2mA Out Q2 2N3904 C1 R3 10k R5 1k8 In 10H (i) Perform DC analysis and prove that the indicated voltages and currents in the figure are correctly calculated. Find the operating point of Q1 and Q2 (5 marks) (ii) Calculate the gain of this amplifier (5 marks) (iii) In the lab, only...
20 points] Q1. The Stately State Transition Matrix, Ф 16 2 3 13 Consider a state transition matrix, Ф, for a SISO LTI system A1. A- 5 11 10 8 9 76 12 Please determine and justify: (a) Ф(t) for this system A 4 14 15 1 ] (b) Ф(s) for this system A (c) System A's characteristic polynomial (d) Ф(z) for this system A via Tustin's method (ie, trapazoid-rule) (e) A difference equation assuming: (1) a step input at...
Hi, I require assistance please. Question: Consider the linear system of differential equations y'1 = 8y1 - 10y2 y'2 = 5y1 -7y2 1. Find the eigenvalues of the coefficient matrix and corresponding eigenvectors. 2. Solve the system. 3. Find the solution that satisfies the initial condition y1(0) = -1, y2(0) = 3 Thank you leamontanotechu.ca/courses/6933/assignments:/44802 = 10046.202005XLIST Assignments Assignment 4 - Due Friday July 31 before 3pm Spring 2030 Assignment 4 - Due Friday July 31 before 3pm Submit Assignment...