The mass m is attached to a spring of free length b and stiffness k. The coefficient of friction between the mass and the horizontal rod is u. The acceleration of the mass can be shown to be x= -f (x), where k f(x)= µg+ b |b² + x° If the mass is released from rest at x = b, its speed at x = 0 is given by Vo = 1. Compute vo by numerical Simpson's 1/3 and 3/8 integration and compare between them with different step size, using the data m = 0.9 kg, b= 0.6 m, µ=0.3, k = 100 N/m, and g = 9.81 m/s?,
The mass m is attached to a spring of free length b and stiffness k. The coefficient of friction between the mass and the horizontal rod is u. The acceleration of the mass can be shown to be x= -f (x), where k f(x)= µg+ b |b² + x° If the mass is released from rest at x = b, its speed at x = 0 is given by Vo = 1. Compute vo by numerical Simpson's 1/3 and 3/8 integration and compare between them with different step size, using the data m = 0.9 kg, b= 0.6 m, µ=0.3, k = 100 N/m, and g = 9.81 m/s?,
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Transcribed Image Text:Case 4: Spring Mass Problem:
The mass m is attached to a spring of free length b and stiffness k. The coefficient of friction
between the mass and the horizontal rod is u. The acceleration of the mass can be shown to be
x= -f (x), where
k
f(x)= ug +
b
m
b² +x?
If the mass is released from rest at x = b, its speed at x 0 is given by
Vo =
V2) f(x)dx
1. Compute vo by numerical Simpson's 1/3 and 3/8 integration and compare between them
with different step size, using the data m = 0.9 kg, b = 0.6 m, u=0.3, k = 100 N/m, and g
= 9.81 m/s?,
2. Develop a MATLAB code to solve the equation for both methods.
3. Plot the acceleration of the mass versus x, and find the area under the curve by MATLAB
built-in function.
4. Can we find an exact solution???Try it.
wwww
Figure (1)
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