{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

247_pdfsam_math 54 differential equation solutions odd

247_pdfsam_math 54 differential equation solutions odd -...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Exercises 4.9 Substitution into the original equation yields m ( 2 cos γt 2 sin γt ) + k ( A cos γt + B sin γt ) = F 0 cos γt A ( 2 + k ) cos γt + B ( 2 + k ) sin γt = F 0 cos γt A = F 0 / ( k 2 ) , B = 0 y p ( t ) = F 0 k 2 cos γt. Therefore, a general solution to the original equation is y ( t ) = C 1 cos ωt + C 2 sin ωt + F 0 k 2 cos γt . With the initial conditions, y (0) = y (0) = 0, we get y (0) = C 1 + F 0 / ( k 2 ) = 0 , y (0) = ωC 2 = 0 C 1 = F 0 / ( k 2 ) , C 2 = 0 . Therefore, y ( t ) = F 0 k 2 cos ωt + F 0 k 2 cos γt , which can also be written in the form y ( t ) = F 0 k 2 (cos γt cos ωt ) = F 0 m ( ω 2 γ 2 ) (cos γt cos ωt ) . (b) Here one can apply the “difference-to-product” identity
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern