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midterm-review - 1 Consider a Simple Pendulum consisting of...

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1) Consider a Simple Pendulum, consisting of a massless string of Length L and a point mass bob, released from rest at an angle ( THETA max). a)Assuming the THETA max is small Find the speed of the bob as it passes through THETA =0. b)Using conservation of energy, find the "exact" speed. c) Using the small angle approximation SHOW that answers (a) and (b) are equivalent. d) repeat part (a) but consider the bob to have spherical dimensions with Radius (r) and an uniformly distributed mass. E) Determine the Velocity for each case if [ L=.5m, THETA max=.5 rad (~28degrees), r=.02m)] 2) A Rope of length (L) hangs vertically from a ceiling. A quick jolt is given to the bottom of the rope causing a wave to propagate up the rope. a) is the speed of propagation constant through the trip. b) Calculate the time it takes for the wave to return to it's orginal position. (hint: reflected wave = incident wave) 3) A Mass (m=10) connected to two springs in series with spring constants (k1=2) and (k2=3), is being driven by an external force ( F ext =F*Sin( OMEGA
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