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hw4_OCW

# hw4_OCW - 16.61 Prof J P How Prof J Deyst Handout#4 March 6...

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16.61 Prof. J. P. How Prof. J. Deyst Handout #4 March 6, 2003 Due: March 13, 2003 16.61 Homework Assignment #4 1. Consider the spring pendulum analyzed before. The arm attached to the rotating shaft has length d = 0 . 8m, as shown in the figure. The shaft is rotating with a constant angular velocity Ω = 0 . 4 rad/sec, but the pendulum is free to change length ( L ) and swing ( θ ). Given that the spring constant is k and the mass of point P is m , find the equations of motion for this system. Note that gravity acts. Pay special attention to Frame selection and FARM. 2. A pendulum of mass m and length l is in a uniform gravitational field. The support point is moving in the vertical direction with a displacement d ( t ), which is a known function of time (Both ˙ d ( t ) and ¨ d ( t ) are known as well). (a) Use Newton’s method to solve for the equations of motion of this system. What frames would be useful to select to solve this problem? Assume small angles.

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hw4_OCW - 16.61 Prof J P How Prof J Deyst Handout#4 March 6...

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