ms.Find a linear operating point model of the differential equation:d²xdx+ 3+ 2x= sin xdt²dta) at xo = 0b) at xo = T

Consider the provided question, Given D.E, d2xdt2+3dxdt+2x=sinx We need to find a linear operating…

Answered: Find a linear operating point model of…

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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ms.
Find a linear operating point model of the differential equation:
d²x
dx
+ 3
+ 2x
= sin x
dt²
dt
a) at xo = 0
b) at xo = T

Expert Solution

Step 1

Consider the provided question,

$G i v e n D . E, \frac{d^{2} x}{d t^{2}} + 3 \frac{d x}{d t} + 2 x = \sin x$

We need to find a linear operating point model of the given D.E at $x_{0} = 0 and at x_{0} = π$

(a)

$S i n c e, \frac{d^{2} x}{d t^{2}} + 3 \frac{d x}{d t} + 2 x = \sin x L i n e a r i z e a b o u t x_{0} = 0 L e t f (x) = \sin x \Rightarrow f (x_{0}) = \sin x_{0} = \sin 0 = 0 S o, \frac{d^{2} x}{d t^{2}} + 3 \frac{d x}{d t} + 2 x = 0$

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