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hw5_ocw

# hw5_ocw - connected in parallel In the ﬁgure φ ˙ is...

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16.61 Handout #5 Prof .J. P .How March 13, 2003 Prof. J. Deyst Due: March 20, 2003 16.61 Homework Assignment #5 1. Consider the catapult problem covered in class, but this time include the eﬀect of gravity and add a twist . The catapult shown has a constantly increasing elevation angle, θ , and a constant rotation rate, about the vertical axis. Derive the equations of motion for the particle. 2. A particle moves in space subject to the constraint: dz =( x + y ) dy +( y +3 x ) dx .Is this constraint holonomic? How many degrees of freedom does the particle have? Find z = f ( x, y ) or if you can not, explain why there is no

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˙ 3. Consider a spherical pendulum with a spring and damper
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Unformatted text preview: connected in parallel. In the ﬁgure, φ ˙ is positive up the page, θ ˙ is positive going into the page. Using spherical coordinates r, θ, φ derive the equations of motion for the mass. For the initial conditions listed, describe the motion of the pendulum after a long time. (Neglect air resistance.) ˙ 3 π r = L, r = L, θ = 4 , θ ˙ = 0 , φ = 0 , φ ˙ = 0 4. Do problem 6.8 of Greenwood’s Principles of Dynamics 2...
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hw5_ocw - connected in parallel In the ﬁgure φ ˙ is...

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