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Solutions02 - PHYS 3113 — Analytical Mechanics Fall 2011...

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Unformatted text preview: PHYS 3113 — Analytical Mechanics Fall 2011 Exam 2 Problem 2.1 [35 pts) An undamped oscillator has a period of 1:0 = 1.0005. If we add a little damping so that its period changes to t1 = 1.0055: a) What is the damping factor, v? (assume that v < can) b) Is this motion under damped, over damped, or critically damped? c) By what factor will the amplitude of the oscillation decrease after 10 cycles? d) Which effect of damping would be more noticeable, the change in period or the decrease in amplitude? Problem 2.2 (30 pts) Consider the force '* = -0:ng + )2?) where a is a constant. Is this force conservative, justify? if a particle of mass m is released from rest at the point (1, 2, 0) and travels under this force toward the origin, how fast is the particle moving at the origin? Problem 2.3 (35 pts) Consider a perfectly frictionless, flat merry-go-round, which is rotating counterclockwise with angular velocity (0 about its vertical axis. A long—armed spectator who is standing on the ground leaning over the merryego~round releases a hockey puck (a small, flat disk) of mass m from rest a distance R out from the center. a] Describe the puck’s path as seen from above by an inertial observer. b] Describe the puck's path as seen from someone traveling with the merry—gee round (a person clamped to the surface). c) What is the velocity of the puck in the noninertial frame of the merry-go-round? d] Compute the centrifugal and Coriolis forces acting on the puck. e) What is the net acceleration in the inertial and noninertial frames? A; if a. w; x @ 2 _ ; W 23f , _ kc a m. _ _ #2., g _, 5 a .5? x451, ...
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