Math21a Fall 2014 HW 32 Solutions - __ Homework__ 32 Flux integral.

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*Homework**32 Flux integral This*

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*homework*RSM Shrewsbury * Homework* That is, the crankshaft of the en- gine rotates at constant angular velocity while each piston moves back-and-forth in its cylin- der according to the rules of simple harmonic motion. 1 cm Suppose the two extremal positions x max and x min of a piston are 10 . When the crankshaft of the engine rotates at 4890 rpm (revolutions per minute), what is the maximal speed | v | max of the piston? (1), x max = x middle A, x min = x middle- A, (3) hence the distance between the extremes x max- x min = 2 A.

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**homework**RSM Wellesley * Homework*. In magnitude, the maximal speed of the piston is | v | max = A (7) = (5 .

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*homework*HippoCampus - __ Homework__ and Study Explanation: Although a piston in a car engine is not by itself a harmonic oscillator, the crank con- necting it to the rotating crankshaft imposes the simple harmonic motion on the piston x ( t ) = x middle A cos( t ) (1) with the angular frequency equal to the angular velocity of the rotating crankshaft. To find out the amplitude for the piston at hand, consider the extreme ponts of the pistons motion: Ac- cording to Eq. The best multimedia instruction on the web to help you with your

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__(1) WRT time, we find v ( t ) = d x dt =- A sin( t ) , (6) which ranges between A and- A .__

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