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Unformatted text preview: (b) Find the ²rst six terms (i.e., up to and including the coe³cient of x 5 ) of the particular solution that satis²es the initial conditions y (0) = 1 and y ′ (0) = 2. 3. (12 pts.) The motion of a simple rigid pendulum without friction can be described by the di±erential equation d 2 θ/dt 2 =K sin θ where K > 0 and θ is the angle the pendulum makes with the downward vertical. (a) Let ω = dθ/dt . Show that d 2 θ/dt 2 = ω dω/dθ . (b) It follows from (a) that the pendulum equation can be written ω dω/dθ =K sin θ . Solve this equation. 4. (10 pts.) Given that y ′′y = g ( t ), y (0) = 1, y ′ (0) = 2 and g ( t ) = b 1t for 0 ≤ t ≤ 1 for t ≥ 1, ²nd Y ( s ), the Laplace transform of y ( t ). END OF EXAM...
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This note was uploaded on 06/18/2009 for the course MATH 20D taught by Professor Mohanty during the Fall '06 term at UCSD.
 Fall '06
 Mohanty
 Math, Differential Equations, Equations

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