HW6_soln - fhb 14 Section 4.7 Problem 18 We started with...

Info icon This preview shows pages 1–5. Sign up to view the full content.

Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

fhb 14
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Section 4.7 Problem 18 We started with the differential equation: ݔ ᇱᇱ ൅ 2ݔ ൅ 2ݔ ൌ cos ሺ2ݐሻ where the right hand side ܨሺݐሻ ൌ cos ሺ2ݐሻ is the external force acting on the system. From the analysis, we saw that the general solution is: ݔሺݐሻ ൌ ଵ଴ ݁ ି௧ cosሺݐሻ ൅ ଵ଻ ଵ଴ ݁ ି௧ sinሺݐሻ െ ଵ଴ cosሺ2ݐሻ ൅ sinሺ2ݐሻ Any terms that contain an exponential to a negative power (i.e. ݁ ି௧ terms in the above equation) will go to zero as we increase ݐ . These terms form the transient component of the general solution; they are the part of the solution that becomes negligible as ݐ increases. The following is an example of the transient component versus the steady state component of a general solution. Say you excite an electric circuit with a time varying voltage; there will be a large initial change in voltage (and current) throughout the circuit. As time goes on, the circuit gets used this input voltage
Image of page 4
Image of page 5
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