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(a) The speed of a motor supplied with a voltage input of 30V, assuming the system is without damping, can be expressed as: 30-(002)쓰-(0.00w If the initial speed is zero and a step size of h = 0.4 s, determine the speed w at r= 0.8 s by: O using Euler's method, and (ii) using the Runge-Kutta 2nd order Heun's method. Given: Euler's method: W - w, + f(t, w, h Heun's method: W - w - where, k = f(t, w) and k = f(t + h. w; + k,h) (b) The exact solution of the ordinary differential equation is w(0.8) = 454.64 rad/s. Explain your result by comparing with the exact solution, and suggest how to reduce the error bethween your result and the evact solution

(a) The speed of a motor supplied with a voltage input of 30V, assuming the system is without damping, can be expressed as: 30-(002)쓰-(0.00w If the initial speed is zero and a step size of h = 0.4 s, determine the speed w at r= 0.8 s by: O using Euler's method, and (ii) using the Runge-Kutta 2nd order Heun's method. Given: Euler's method: W - w, + f(t, w, h Heun's method: W - w - where, k = f(t, w) and k = f(t + h. w; + k,h) (b) The exact solution of the ordinary differential equation is w(0.8) = 454.64 rad/s. Explain your result by comparing with the exact solution, and suggest how to reduce the error bethween your result and the evact solution

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) The speed of a motor supplied with a voltage input of 30V, assuming the system is without damping, can be expressed as: 30 = (0.02)-(0.06w dt If the initial speed is zero and a step size of h = 0.4 s, determine the speed w at t 0.8 s by: O using Euler's method; and (i) using the Runge-Kutta 2nd order Heun's method. Given: Euler's method: W - w, + f(t, w, h Heun's method: W - w, + where, k = f(4.w) and k = f(t; + h, w; + k, h) (b) The exact solution of the ordinary differential equation is w(0.8) = 454.64 rad/s. Explain your result by comparing with the exact solution, and suggest how to reduce the error between your result and the exact solution.
Transcribed Image Text:(a) The speed of a motor supplied with a voltage input of 30V, assuming the system is without damping, can be expressed as: 30 = (0.02)-(0.06w dt If the initial speed is zero and a step size of h = 0.4 s, determine the speed w at t 0.8 s by: O using Euler's method; and (i) using the Runge-Kutta 2nd order Heun's method. Given: Euler's method: W - w, + f(t, w, h Heun's method: W - w, + where, k = f(4.w) and k = f(t; + h, w; + k, h) (b) The exact solution of the ordinary differential equation is w(0.8) = 454.64 rad/s. Explain your result by comparing with the exact solution, and suggest how to reduce the error between your result and the exact solution.
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