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Task 3: Description [100 Marks] The rate of change of the temperature of the coffee is...
MATLAB CODE:
Task 2 8y dt Solve the above ordinary differential equation (ODE) using Euler's method with step sizes of: 2. h 0.75 3. h 0.5 4. h 0.001 a) For each step size, plot the results at each step starting from y(0) 3 to y(3). b) Plot on the same figure as part a) the analytical solution which is given by: 9 24 -8t c) Calculate and print the percentage error between the Euler's method and the analytical result...
(30 pts) Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature). dT * = -k(T – Ta) where T = the temperature of the body (°C), t = time (min), k = the proportionality constant (per minute), and Ta = the ambient temperature (°C). Suppose that a cup of coffee originally has a temperature of 80 °C. Use...
The temperature T (K) of a steel ball in a hot stream of air can be modeled with the tollowing t order ordinary differential equation of temperature T (K) with respect to time t (seconds) dT where p is the mass density (7854 kg/m3) c is the specific heat (434 J/(kg-K) Lc is the characteristic length (m) havg is the average convection heat transfer coefficient (25 W/(m2-K) Tin is the temperature of the surrounding fluid (75 K) The characteristic length...
please I’m having trouble with for a 4 a& b . The first picture
is my work
HS kt 00Ce 0-8001 L0 0 요) t20 ute thange in volume. 4. A thin plate is heated to 100 Cfor purposes of sterilization and then it is placed inside a room kept at a constant temperature of 20 C where i is allowed to cool down. The rate of change of the temperature of the plate, T,with respect to (a) Solve this...
Exercise 3 is used towards the question. Please in MATLAB
coding.
1. Apply Euler's Method with step size h=0.1 on [0, 1] to the initial value problems in Exercise 3. Print a table of the t values, Euler approximations, and error (difference from exact solution) at each step. 3. Use separation of variables to find solutions of the IVP given by y) = 1 and the following differential equations: (a) y'=1 (b) y'=1y y'=2(1+1)y () y = 5e4y (e) y=1/92...
I am really confused as to how I can even approach this
differential equation, I really need a step by step solution.
Thanks!!
406 Chapter 5 Differential Equations 5 Performance Task Spread of an Influenza Virus Throughout history, influenza viruses have caused pandemics or global epidemics. The influenza pandemic of 1918-1919 occurred in three waves. The first wave occurred in the late spring and summer of 1918, the second wave occurred in the fall of 1918, and the final wave...
using matlab thank you
3 MARKS QUESTION 3 Background The van der Pol equation is a 2nd-order ODE that describes self-sustaining oscillations in which energy is withdrawn from large oscillations and fed into the small oscillations. This equation typically models electronic circuits containing vacuum tubes. The van der Pol equation is: dt2 dt where y represents the position coordinate, t is time, and u is a damping coefficient The 2nd-order ODE can be solved as a set of 1st-order ODEs,...
5. Numerical Integration (15 marks] When a charged particle moves perpendicular to a magnetic field it traces out circles in the plane perpendicular to the magnetic field due to the "Lorentz force". Here we consider a small particle (e.g. dust grain or nanoparticle) with a charge to mass ratio of 1 Coulomb per kg moving perpendicular at speed v1 = 1 m/s to a 1 Tesla magnetic field that points in the z direction. In this case the motion is...
Please
help me with this short, matlab/diffy q project.. teacher said it’s
supposed to be a short code
Matlab Project Recall that we can approximate the time derivative of a function y(t) at time tn as dt ΔΙ This follows from the limit definition of the derivative and gives the approximate slope of the function y(t) at time tn If we think about 'stepping through time from some initial time to a later time in steps of size At, then...
2. Let L(t) = the length (in cm) of a fish at time t (in years). Suppose that the fish grows at a dL dt = 5.0e-0.2t rate (a) Determine the exact change in length of the fish between times t 5 and t 10. (Suggestion: First solve the differential equation using anti-differentiation.) Does the answer to this question depend on the initial condition L(0)? (b) Determine L(t) if L(0)=2 2. Continued (c) Find the approximate change in length of...