The circle is horizontal such that gravity can be

Info icon This preview shows pages 2–4. Sign up to view the full content.

ignore any effects related to the curvature. The circle is horizontal such that gravity can be ignored. a. Find equations of motion for the three masses in terms of the small displacements from the equilibrium position of each mass. b. Determine the frequencies and the relative amplitudes for each of the normal modes. Make a simple sketch of the motion of the masses for each of the normal modes. How many different frequencies are there in this system? c. Because the masses are connected in a circle some of the results of normal mode calculations do not correspond to oscillatory motion. Explain why. 2
Image of page 2

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

k k m m h(t) y (t) y (t) 1 2 Figure 3: Two Masses Hanging from an Oscillating Support Problem 3.4 (20 pts) Consider two identical masses m connected together with a spring and attached with another spring to a moving support (see Figure 3). The support is oscillating vertically and its position is given by h ( t ) = A cos( ωt ). The Hooke constant of the two identical springs is k . Ignore effects of damping. a. Find coupled differential equations that govern displacements from equilibrium of the masses y 1 ( t ) and y 2 ( t ). Express your results in terms of ω 2 0 = k m . Note that the effect of gravity results in a shift of equilibrium position but it does not affect the harmonic motion.
Image of page 3
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.
  • Spring '14
  • Massachusetts Institute of Technology, normal modes

{[ 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