Find the solution to the initial value problem: x" + 25x = (µ+5)cos µt x(0) = 0 x'(0) = 0 1 1 x(t) = µ – 5 µ -5COS(ut) | x Write x(t) as a product of two sines, one with the beat (slow) frequency (µ – 5)/2 , and the other with the carrier (fast) frequency (µ+ 5)/2. x(t) = The solution x(t) is really a function of two variables t and u. Compute the limit of x(t,µ) as µ approaches 5 (your answer should be a function of t). lim x(t,u) = Define y(t) = lim x(t,u) Now let u approach 5 in the differential equation satisfied by x(t) to find a differential equation that y(t) satisfies. y" + y =
Find the solution to the initial value problem: x" + 25x = (µ+5)cos µt x(0) = 0 x'(0) = 0 1 1 x(t) = µ – 5 µ -5COS(ut) | x Write x(t) as a product of two sines, one with the beat (slow) frequency (µ – 5)/2 , and the other with the carrier (fast) frequency (µ+ 5)/2. x(t) = The solution x(t) is really a function of two variables t and u. Compute the limit of x(t,µ) as µ approaches 5 (your answer should be a function of t). lim x(t,u) = Define y(t) = lim x(t,u) Now let u approach 5 in the differential equation satisfied by x(t) to find a differential equation that y(t) satisfies. y" + y =
Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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
Transcribed Image Text:Find the solution to the initial value problem:
x" + 25x =
(u+5)cos µt
x(0) = 0
x'(0) = 0
%3D
1
1
cos(
5COS(ut) x
x(t)
Write x(t) as a product of two sines, one with the beat (slow) frequency (u – 5)/2 , and the other with the carrier (fast) frequency (µ+ 5)/2.
x(t) =
The solution x(t) is really a function of two variables t and u. Compute the limit of x(t,µ) as µ approaches 5 (your answer should be a function of t).
lim x(t,u)
Define y(t)
= lim x(t,u) Now let u approach 5 in the differential equation satisfied by x(t) to find a differential equation that y(t) satisfies.
y" +
у 3
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