Chapter13-page3 - L 3 are excited Energy of the String...

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

View Full Document Right Arrow Icon
Physics 235 Chapter 13 - 3 - The initial conditions are q x ,0 ( ) = 3 h L x , 0 ! x ! L 3 3 h 2 L L " x ( ) , L 3 ! x ! L # $ % % % % (1) ! q x ,0 ( ) = 0 (2) Because ! q x ,0 ( ) = 0 , all of the ! r vanish. The μ r are given by μ r = 6 h L 2 x sin r ! x L dx 0 L 3 " + 3 h L 2 L # x ( ) sin r ! x L dx L 3 L " = 9 h r 2 ! 2 sin r ! 3 (3) We see that μ r = 0 for r = 3, 6, 9, etc. The displacement function is q x , t ( ) = 9 3 h 2 ! 2 sin ! x L cos " 1 t + 1 4 sin 2 ! x L # cos " 2 t $ 1 16 sin 4 ! x L cos " 4 t $ % & ( ) * (4) where ! r = r " L # $ (5) The frequencies ! 3 , ! 6 , ! 9 , etc. are absent because the initial displacement at L 3 prevents that point from being a node. Thus, none of the harmonics with a node at
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: L 3 are excited. Energy of the String Since we know the displacement of the string, as function of x and t , q x , t ( ) = s e i s t sin s x L $ % & ’ ( ) s * we can calculate the kinetic energy and the potential energy of the system....
View Full 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