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Unformatted text preview: MthSc 208 (Spring 2011) Worksheet 3c MthSc 208: Differential Equations (Spring 2011) In-class Worksheet 3c: Harmonic motion
NAME: When a 2 kg mass is hung from a spring, the spring is displaced by 0.5 m. Now, suppose that the mass is displaced an additional 0.12 m downward from this equilibrium, and then released. We will set up and solve an initial value problem that models this. (a) Sketch this mass-spring system, before and after the mass is place on the spring. (Let x = 0 be the height of the spring without the mass). (b) At equilibrium, the spring force kx0 equals the gravitational force, mg, in magnitude. Use this to solve for the spring constant k. (c) Newton's 2nd law tells us that F = mx , which is equal to the sum of the forces (gravitational and spring). Write down a second-order differential equation that models this. Include both initial conditions, x(0) and x (0). Written by M. Macauley 1 MthSc 208 (Spring 2011) Worksheet 3c (d) Find the general solution to this ODE. Is there a steady-state solution? If so, describe it. (e) Solve the initial value problem. (Hint: Use the "simplest" initial condition first). Written by M. Macauley 2 ...
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