8.12.5 problem 5

Internal problem ID [912]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number : 5
Date solved : Monday, January 27, 2025 at 03:18:33 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 60

dsolve(m*diff(x(t),t$2)+k*x(t)=F__0*cos(omega*t),x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {c_1 \left (-m \,\omega ^{2}+k \right ) \cos \left (\frac {\sqrt {k}\, t}{\sqrt {m}}\right )+c_2 \left (-m \,\omega ^{2}+k \right ) \sin \left (\frac {\sqrt {k}\, t}{\sqrt {m}}\right )+F_{0} \cos \left (\omega t \right )}{-m \,\omega ^{2}+k} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 54

DSolve[m*D[x[t],{t,2}]+k*x[t]==F0*Cos[omega*t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {\text {F0} \cos (\omega t)}{k-m \omega ^2}+c_1 \cos \left (\frac {\sqrt {k} t}{\sqrt {m}}\right )+c_2 \sin \left (\frac {\sqrt {k} t}{\sqrt {m}}\right ) \]