302 (S98) Exam #1

302 (S98) Exam #1 -...

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Unformatted text preview: þ7########,###################>########x#######{#####################h#####h##4# ####4#####4#####4##.##8P####8P####8P#(##8x# ##8¡####8¡####8¡#P##8è#x##4F# ##9`# ##9¡####<9#*##<c#u##4#########<#####9¡#m##<#####</# ##=Ø#=##<9####<9####<9####<9####<9####<9####Name 1. [25 points total] Suppose that you are analyzing the motion of a system and obtain the following Lagrangian: #where m, a, b, and wo are all constants.A. [10 pts] Find LagrangeÕs equation (or equations) of motion for the system. As always, show all your work.B. [15 pts] Find the general solution to the equation (or equations) of motion that you found in part A. (By general, I mean do not apply any initial conditions). 2. [25 points total] A uniform rod of moment of inertia I about it center is pivoted at its center. A bead of mass m is placed on the rod and slides without friction. (Note: The system moves in a vertical plane.)A.[6 pts] Find the Lagrangian for this system. B. [14 pts] Find LagrangeÕs equation (or equations) of the motion. Show your work.C. [5 pts] Is the angular momentum of the system conserved? Explain. #3. [25 points total] A block of mass M1 sits on a frictionless table and is connected by a massless, inextensible string to a block of mass M2 that hangs over a frictionless pulley, as shown. Use LagrangeÕs method of undetermined multipliers to find the tension in the string and the acceleration of the system. (Note: all of us can find the tension and the acceleration fairly simply with NewtonÕs laws, so no points will be awarded for correct answers. Only the method used will be graded.)Name Total Points Name Total Points Physics 302 (Spring 1998) First Exam (January 30, 1998)#v#¡##v#¡#######Â#########¡### ´###########¡#¤#######¡##¢#d##·xpr####### ## #¡## #######¡#####"###¡## #¾¢#À#currentpoint #¿"###### #¾,#####Times###### .##ÿ###+# #L,# ###Symbol#####) #=#####(#####1*##2#####"######### (# ###m##(###&#ú ##(# #%#y ####(###+#2#### +###-#####) #ay####(###G#2#### +###+#####) #by##)#cos)##(#####)##w#####+ ##o# (# #¡#t##)##)¢#À#Ò30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 4576 div 544 3 -1 roll exch div scale currentpoint translate 64 63 translate 12 321 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (L) show 325 321 moveto 384 /Symbol f1 (=) show 669 182 moveto 224 /Times-Roman f1 (1) show 669 414 moveto (2) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 643 222 moveto 164 0 rlineto stroke 867 321 moveto 384 /Times-Italic f1 (m) show 1178 303 moveto 384 /Times-Roman f1 (\307) show 1144 321 moveto 384 /Times-Italic f1 (y) show 1331 152 moveto 224 /Times-Roman f1 (2) show 1561 321 moveto 384 /Symbol f1 (-) show 1857 321 moveto 384 /Times-Italic f1 (ay) show 2236 152 moveto 224 /Times-Roman f1 (2) show 2467 321 moveto 384 /Symbol f1 (+) show 2760 321 moveto 384 /Times-Italic f1 (by) show 3168 321 moveto...
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This document was uploaded on 10/29/2011 for the course PHSX 302 at MSU Bozeman.

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302 (S98) Exam #1 -...

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