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

please show work answer is D

kindly create and explain an HOQ Analysis on this

What mathematical relationship exists between the wave speed and the density of the medium, using the POWER trendline equation from the graph? Make your response specific (i.e., describe the full mathematical proportionality between the two variables) Feel free to use the table. Table:  Frequency (Hz) Density (kg/m) Tension (N) Speed (cm/s) Wavelength (cm) 0.85 0.1 4.0 632.5 744.12 0.85 0.7 4.0 239.0 281.18 0.85 1.3 4.0 175.4 206.35 0.85 1.9 4.0 145.1 170.70

Please don't provide handwritten solution.

Example: bottled water at Kroger (Homework) = Month Actual Forecasted α = 0.3 Jan 1,325 1,370 Feb 1,353 1,361 Mar 1,305 1,359 Apr 1,275 1,349 May 1,210 1,334 Jun ? 1,309 solve the acutal sales in jun using Exponential smoothing: the method Assume that we are currently in period. We calculated the forecast for the last period (F) and we know the actual demand last period (4.) ... F₁=F₁₁+a(A₁-F₁) The smoothing constant a expresses how much our forecast will react to observed differences... If a is low: there is little reaction to differences. If a is high: there is a lot of reaction to differences.

= MMB 241- Tutorial 1.pdf 2/3 80% + + 10. Determine a ats = 1 m v (m/s) 4 s (m) 2 11. Draw the v-t and s-t graphs if v = 0, s=0 when t=0. a (m/s²) 2 t(s) 12. Draw the v-t graph if v = 0 when t=0. Find the equation v = f(t) for each a (m/s²) 2 segment. 2 -2 13. Determine s and a when t = 3 s if s=0 when t = 0. v (m/s) 2 t(s) t(s) 2

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?

explains how the two methods of parameter estimation, namely the method of parameter estimation and the method of moments and percentile matching, are used to fit distributions to data for actuarial calculations.

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;…