feb22c - MIT OpenCourseWare http:/ocw.mit.edu 6.055J /...

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

View Full Document Right Arrow Icon
MIT OpenCourseWare http://ocw.mit.edu 6.055J / 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
Background image of page 1

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

View Full DocumentRight Arrow Icon
p 5 Proportional reasoning k x = 0 m x 27 So imagine a mass m connected to the wall by a spring with spring constant k . If disturbed, the mass oscillates. The period of the system is the time for the mass to make a round trip through the equilibrium position. Extend the spring by a distance x 0 ; this displacement is the amplitude. To see how it affects the period, make an approximation, which will be an example of throwing away information (the topic of Part 3 ). The approximation is to pretend that the pendulum moves with a constant speed v . Then the period is distance , T speed v and the distance that the mass travels in one period is 4 x 0 . Ignore the factor of 4: . T x v 0 Proportional reasoning helps us estimate v by an energy argument. The initial potential energy is PE kx 2 0 or PE x 2 0 . The maximum kinetic energy, which we use as a proxy for the typical kinetic energy, is the
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

feb22c - MIT OpenCourseWare http:/ocw.mit.edu 6.055J /...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online