(16) Three Spring-Coupled Masses

# (16) Three Spring-Coupled Masses - Three Spring-Coupled...

This preview shows pages 1–3. Sign up to view the full content.

Three Spring-Coupled Masses Consider a generalized version of the mechanical system discussed in Section 4.1 that consists of three identical masses which slide over a frictionless horizontal surface, and are connected by identical light horizontal springs of spring constant . As before, the outermost masses are attached to immovable walls by springs of spring constant . The instantaneous configuration of the system is specified by the horizontal displacements of the three masses from their equilibrium positions: namely, , , and . This is manifestly a three degree of freedom system. We, therefore, expect it to possess three independent normal modes of oscillation. Equations ( 149 )-( 150 ) generalize to (202) (203) (204) These equations can be rewritten (205) (206) (207) where . Let us search for a normal mode solution of the form (208) (209) (210) Equations ( 205 )-( 210 ) can be combined to give the homogeneous matrix equation

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

View Full Document
(211) where . The normal frequencies are determined by setting the determinant of the matrix to zero: that is, (212) or (213)
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern