Question

Find the (steady-state) periodic solution to the differential equation \[ x^{\prime \prime}+5 x^{\prime}+100 x=6 \sin (2 t) \] in the form \[ X(t)=C \cos (\omega t-\alpha), \] with \( C>0 \) and \( 0 \leq \alpha<2 \pi \).

          Find the (steady-state) periodic solution to the differential equation
\[
x^{\prime \prime}+5 x^{\prime}+100 x=6 \sin (2 t)
\]
in the form
\[
X(t)=C \cos (\omega t-\alpha),
\]
with \( C>0 \) and \( 0 \leq \alpha<2 \pi \).

Find the (steady-state) periodic solution to the differential equation

x^''+5 x^'+100 x=6 sin (2 t)

in the form

X(t)=C cos (ω t-α),

with C>0 and 0 ≤α<2 π.

Added by Larry H.

Engineering Mathematics

Stroud, K. A. Booth, Dexter J. 7th Edition

Chapter 39

Instant Answer

Solved by Expert M Hassan Anwar

03/06/2022

Step 1

Given the differential equation: \[ x'' + 5x' + 100x = 6 \sin(2t), \] we assume a particular solution of the form: \[ x_p(t) = A \cos(2t) + B \sin(2t). \] Show more…

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Find the (steady-state) periodic solution to the differential equation \[ x^{\prime \prime}+5 x^{\prime}+100 x=6 \sin (2 t) \] in the form \[ X(t)=C \cos (\omega t-\alpha), \] with \( C>0 \) and \( 0 \leq \alpha<2 \pi \).