2301-18ps12.pdf - Physics 2301 Problem Set#12 The normal...

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Physics 2301: Problem Set #12 The normal problems are due at the end of the day on Tuesday, April 24. The animation should be uploaded to Carmen by a week later, May 1. 1. Shankar, problem 6.2.6 pg. 121. Also find arccos( 3 4 i ), i.e. express it in x + iy format. 2. Shankar, problem 9.7.4 pg. 284. 3. Morin 6.25 (Spring on a T) p. 251. 4. Morin 6.45 (Mass sliding on a rim) p. 255. 5. Consider a system of 2 equal masses m and 3 springs attached to two walls, as drawn. Note that the springs are not of equal strength. (a) Find the frequencies of the normal modes. (b) Suppose now that in addition to the springs, the right mass is driven by an external force F ( t ) = F 0 cos( q k m t ) (with no driving force on the left mass). If the system starts at t = 0 with both masses at rest at their equilibrium positions, find the motion. That is, find x 1 ( t ) and x 2 ( t ). 6. Consider the space of functions on the interval x (0 , 1). (a) Choose as a basis a set of polynomials of degree
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