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Asg1_Sol

# Asg1_Sol - MATH 118 Spring 2010 Assignment 1 Solutions 1...

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MATH 118 – Spring 2010 Assignment 1, Solutions 1. Textbook, Page 486, Exercises 7.10, # 7, 23a, 31. 2. Textbook, Page 493, Exercises 8.1, # 7, 13, 19. 3. Textbook, Page 498, Exercises 8.2, # 3, 13, 23 (only evaluate L L dx L x n x f cos ) ( ).

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23. 4. Consider the plane pendulum shown in the figure that swings between points A and C. If B is midway between A and C, it can be shown that (g is the acceleration due to gravity) ) ( 2 2 s s g L ds dt C (a) If 0 ) 0 ( t , then show that the time the pendulum takes to travel between points B and P is ) ( sin ) ( 1 C s s g L s t (b) Use the result in part (a) to determine the time of travel from B to C.
(a) ) / ( sin 0 0 ) 0 ( ) / ( sin ) ( ) ( 1 1 2 2 2 2 2 2 C C C C C s s g L t C t C s s g L C s s ds g L C ds s s g L t s s g L ds dt (b) For C s s , we obtain g L g L s t C 2 ) 1 ( sin ) ( 1 . Note that this means the period of the pendulum is
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Asg1_Sol - MATH 118 Spring 2010 Assignment 1 Solutions 1...

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