ME 340 Lab 7 - Nonlinear Systems

Simulink Assignment- Filling a Tank In fluid mechanics, the equation that models the fluid level in a tank is: dh 1 -(min Ap - mout) dt h is the water level of the tank A is the surface area of the bottom of the tank pis the density of the fluid Mim and mout are the mass flow rates of water in and out of the tank, the flow out is a function of the water level h: 1 mout Vpgh Ris the resistance at the exit. Assume that the exit is at the bottom of the tank. g is the gravitational acceleration What to Do: 1. Build a model in Simulink to calculate the water level, h, as a function of time. Your model should stop running as soon as the tank is full. 2. Assuming the height of the tank is 2 meters, after how many seconds does the tank fill up? Use the following constants to test your model: • A: area of the bottom of the tank = 1 m? • p: the density of fluid = 1000 kg/ m? • R: the resistance at the exit = 3 (kg.m)-1/2 • ho: Initial height of the fluid in the tank = 0 m • g: the gravitational…

T'sec In helical spring experiment a student plotted the graph of T2 versus the oscillating mass (M), and Used the slope to find the spring :constant, the value of k is 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 O. O a. 13.3 N/m O b. 6.8N/m O c. 5 N/m O d. 3.3 N/m O e. 24 N/m 5 10 15 20 25 30 35 40 45 50 55 60 65 M (9) 70 75 80

The governing equation of motion for a base motion system is given by (assume the units are Newton) mä(t)+ci(t)+kx(t) =cY@, cos(@,t) +kY sin(@t) %3D Given that m = 180 kg, c = 30 kg/s, Y = 0.02 m, and о, — 3.5 rad/s %3| 1. Use Excel or Matlab to find the largest value of the stiffness, k that makes the transmissibility ratio less than 0.85 2. Using the value of the stiffness obtained in part (1), determine the transmitted force to the base motion system using Matlab or Excel. 3. Display and discuss your results.

Determine the coefficients (a and b) for the baseflow (Qb) in using the data below. Find values for a and b that satisfy the given equation shown below.  Present the figures or plots utilized during the estimation and determination of a and b. Compare the obtained b value with theoretical values such as b = 1 and b = 1.5 for large time intervals (t), and b = 3 for small time intervals.

Manufacturing process with two variables x1,x2 described by the empirical model:   y=bo +b1 x1 + b2 x2 + b12 x1 x2 + b3 (x1)^2 +b4  (x2)^2    please refere to the image attached

B) Analyze the following frequency responses of a first-order system subject to a simple periodic input of the form Asin(wt). 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.01 0.10 L 1.00 τω 10.00 0 -2 -10 -20 100.00 0 -10 -20 -30 -40 -50 -60 -70 -80 -90 0.01 0.1 1.0 TW 10.0 100.0 C) Which would you expect to be better suited to measure a time-dependent temperature, a thermal sensor (e.g., a thermocouple) having a small diameter spherical bead or one having a large diameter spherical bead? Explain your choice using a mathematical expression or model. D) Determine the 95 % response time for the system 5 y + 5y = U(t), where, U(t) = { iftst 1 t'

Give MATLAB commands to plot, on the same figure, the two functions: f=3 r +2t- 0.5 g = 2 t cos(t) Where the variable t varies from 0 to 10 with step 0.5

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11. In step of FEM a discrete model is generated from a mathematical model. (a) Preprocessing (b) Discretization(c) Validation(d)interpolationif not sure skip may downvote if wrong

kindly create and explain an HOQ Analysis on this

look at the graph wich presents F vs x graph ...  Q : Determine the compression of the spring from the change in position of the cart+block in Graph ? please tell me the steps how can I find compression of the spring from the change in position of the cart+block

mathforadmi..2dff1dd723 PTU Kadoorie sygini 1930 Technical Department of Applied Mathematics Second Semester 2020/2021 Math for Administration Assignment 2 Question 1 For the function: y = 0.01x- 0.001x² Find the zeros, the vertex and the optimum value (max. or min.) Question 2 Suppose a company has fixed costs of $300 and variable 3 costs of x + 1460 dollars per unit, 4 where x is the total number of units produced. Suppose further that the selling price of its product is 1500 X- ♡ lar Fine break-even points. init. II جامعة Palestine ||

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Harmonic oscillators. One of the simplest yet most important second-order, linear, constant- coefficient differential equations is the equation for a harmonic oscilator. This equation models the motion of a mass attached to a spring. The spring is attached to a vertical wall and the mass is allowed to slide along a horizontal track. We let z denote the displacement of the mass from its natural resting place (with x > 0 if the spring is stretched and x 0 is the damping constant, and k> 0 is the spring constant. Newton's law states that the force acting on the oscillator is equal to mass times acceleration. Therefore the differential equation for the damped harmonic oscillator is mx" + bx' + kr = 0. (1) k Lui Assume the mass m = 1. (a) Transform Equation (1) into a system of first-order equations. (b) For which values of k, b does this system have complex eigenvalues? Repeated eigenvalues? Real and distinct eigenvalues? (c) Find the general solution of this system in each case. (d)…

ques 4  plz provide handwritten step by step answer asap

Vibrations

Problem 1 (15 points) (Core Course Outcome 5)/MatlabGrader Write a function mySecond Derivative Order 3 that calculates the second derivative d²y/dx² of a data set (x, y) with at least third order accuracy at each data point. The data is equidistant in x with spacing h. The function input shall be ⚫y: one-dimensional column vector of y values ⚫h: scalar value of spacing h The function output shall be • d2y: column vector of the same size as y containing d²y/dx² Calculate d²y/dx² using only the following formulas that use the nomenclature of Table 8-1 and the lecture notes, but are different from the formulas listed there: f" (xi) 164f(xi) — 465f(xi+1) + 460ƒ (xi+2) − 170ƒ (xi+3) + 11f (xi+5) + O(h³) = 60h2 56f(xi−1) − 105f(xi) +40f(xi+1) + 10f(xi+2) − f(x+4) + O(h³) 60h² −5f(xi−2) +80f(xi−1) − 150f(xi) + 80f(xi+1) − 5ƒ(xi+2) (1) f"(xi) = (2) f"(xi) = +0(h) (3) 60h2 f"(xi) -2f(x-4)+5f(xi-3)+50f(xi-1) — 110f(xi) +57f(xi+1) = +0(h³) (4) 60h² f"(xi) = 57f(x-5) 230f(xi-4) + 290 f (xi-3)-235…

Can you help me solve the following problem in MATLAB?

PIoVide ue comect u We want to design an experiment to measure oscillations of a simple pendulum on the surface of Jupiter with acceleration due to gravity g= 30 ms 2. We have to make do with a rudimentary video camera with a frame rate of 15 Hz to record oscillations in a pendulum and use it to measure the frequency of oscillation. The smallest length of the pendulum that we can send so that the correct oscillation frequency can be measured is cm. Assume perfect spatial resolution of the camera and ignore other "minor" logistical difficulties with this experiment.

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I am trying to compute the probability of collision with the monte carlo method in MATLAB. But I get an error in teh following code. The error is the matrix P_01 must be semi definete and P_02 must be symmetric. How should I fix this problem?   % Initial Mean and Covariance mu_01 = [153446.180; 41874155.872; 0; 3066.875; -11.374; 0] / 1000; P_01 = [6494.080 -376.139 0 0.0160 -0.494 0; -376.139 22.560 0 -9.883e-4 0.0286 0; 0 0 1.205 0 0 -6.071e-5; 0.0160 -9.883e-4 0 4.437e-8 -1.212e-6 0; -0.494 0.0286 0 -1.212e-6 3.762e-5 0; 0 0 -6.071e-5 0 0 3.390e-9] * 1e-6;   mu_02 = [153446.679; 41874156.372; 5.000; 3066.865; -11.374; -1.358e-6] / 1000; P_02 = [6494.224 -376.156 -4.492e-5 0.0160 -0.494 -5.902e-8; -376.156 22.561 2.550e-6 -9.885e-3 0.0286 3.419e-9; -4.492e-5 2.550e-6 1.205 -1.180e-10 3.419e-9 -6.072e-5; 0.0160 -9.883e-3 -1.180e-10 4.438e-8 -1.212e-6 -1.448e-13; -0.494 0.0286 3.419e-9 -1.212e-6 3.762e-5 4.492e-12; -5.902e-8 3.419e-9 -6.072e-5 -1.448e-13 4.492e-12 3.392e-9] * 1e-6;…

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The 2nd order ODE given below models the vertical fall of on Object under the influence of gravity and air friction md²y acceleration -mg + (1/2 Co A Pair) (dy) ² Forcing due logranty Forcing due to air friction

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