b) An undamped oscillation under the influence of external : by dr UTM&UTM + kr = dt? %3D O UTM U and spring constant k and let w mas F(t) = Fo cos (wot), where wo # w. What type of value k and m so that the corresponding homogeneous solution is m %3D with external force m UTM UTM UTM an(t) = A cos(wt)+ B sin(wt)? Hence, by using the method of undetermined coefficients, show that AUTM UTM UTM r(t) = A cos(wt) + B sin(wt) + Fo m(w? – wi) cos (wnt).

b) An undamped oscillation under the influence of external : by dr UTM&UTM + kr = dt? %3D O UTM U and spring constant k and let w mas F(t) = Fo cos (wot), where wo # w. What type of value k and m so that the corresponding homogeneous solution is m %3D with external force m UTM UTM UTM an(t) = A cos(wt)+ B sin(wt)? Hence, by using the method of undetermined coefficients, show that AUTM UTM UTM r(t) = A cos(wt) + B sin(wt) + Fo m(w? – wi) cos (wnt).

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

b) An undamped oscillation under the influence of external
by
UTM &UTM &U
+ kr =
dt2
TM
and spring constant k and let w
UTM
F(t) = Fo cos (wot), where wo # w. What type of value k and m
mas
so that the corresponding homogeneous solution is
with external force
m
SUTM
an(t) = A cos(wt)+ B sin(wt)?
Hence, by using the method of undetermined coefficients, show that
UTM
AUTM UTM
UTM
r(t) = A cos(wt) +B sin(wt) +
%3D
Fo
UTM
m(w? – wi)
cos (unt).

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