{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# PS6 - Prof Raghuveer Parthasarathy University of Oregon...

This preview shows pages 1–2. Sign up to view the full content.

Prof. Raghuveer Parthasarathy University of Oregon; Fall 2007 Physics 351 – Vibrations and Waves Problem Set 6 Due date: Friday, Nov. 16, 4pm. Reading: French Chapter 5. A note: This problem set is shorter than it seems. Problems 2-6 are very similar to one another, which should cement your understanding of coupled oscillators and should also be useful in analyzing the coupled oscillator systems that you build. Problem 1 is not related to coupled oscillators and could have been assigned weeks ago. (1, 6 pts. ) Phase space. It’s often informative to consider the trajectory of a system in “phase space,” in which particular physical quantities form the coordinate axes. One common set of quantities is position and velocity. For example : let’s imagine some system in which the position is given by () / x ta t = , and the velocity is given by 2 / vt x a t == ± , where t is time and a is some constant. Therefore 2 / va x =− – i.e. vx is a quadratic function of x . At time t =0, both v and x are zero, so our parabola “starts” at the origin of our phase space plot. The plot looks like: (a, 3 pts. ) Consider an undamped simple harmonic oscillator. Prove that the phase space plot (with axes x and x ± ) is an ellipse. (Remind yourself of the equation characterizing an ellipse.) (b, 2 pts. ) Draw the phase space plot for an undamped oscillator with the initial conditions 0 (0 ) t x x = = , ) 0 t v = = . Indicate the t =0 point on the plot. (b, 1 pt. ) What would the phase space plot of a damped oscillator look like? Draw it, qualitatively – you don’t have to do any math. Indicate the “t= ” point on the plot. (2 , 12 pts ) Two coupled masses. Consider two objects ( A and B ) of equal mass m connected to each other and to rigid walls by identical springs of spring constant k (see Figure). Neglect damping, and assume all motion is in a horizontal plane, so gravity is irrelevant.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

PS6 - Prof Raghuveer Parthasarathy University of Oregon...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online