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Unformatted text preview: Math 201 Assignment # 6 Due: Nov. 8 in tutorial • Grade problems 3 and 4, 10 points each for a total of 20. 1. A 1 kg mass is suspended from a spring with a spring constant of k = 5 N/m. The surrounding medium offers a damping force equal to 2 times the velocity. At time t = 0 s, the mass is released from a position 1 m below equilibrium with a downward velocity of 2 m/s. At the same time, a source is switched on which drives the spring with a force f ( t ) = 3cos2 t +5sin2 t . (a) Set up a differential equation modelling the position of the mass, including initial conditions. (b) Solve the IVP in (a) to obtain the equations of motion. (c) As t → ∞ one part of the solution, the transient term, decays to 0. The term which does not decay, the steady state, is purely oscillatory. By rewriting this term as A sin( kt + φ ), identify its amplitude. • This springmass system satisfies the differential equation: 1 d 2 x dt 2 + 2 dx dt + 5 x = 3cos2 t + 5sin2 t Since we consider the position below equilibrium to be positive, our...
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 Winter '10
 STEACY
 Math, Laplace, Cos, PierreSimon Laplace

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