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| Phy 340 page |
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6 Oct The R-L-C circuit with sinusoidal forcing. The equations are the same as for a mass on a spring with viscous damping. Solve the equations again, and note the terminology of transient and steady-state and the reason for it. Sketch the resonance curve.
What happens when a mass is suspended from four springs in two dimensions? The equations of motion lead to oscillations in the x- and y-directions, and can start to get complicated. Solve the problem and show some of the preliminary special cases: circle, ellipse, line, Lissajous figure.
8 Oct Compute the escape speed from the Earth.
The trajectory of an object thrown through the air, including in the calculation the frictional force from the air. For simplicity, assume that the friction is linear in the velocity: - m g v. This assumption is used, not because it is the most realistic (it isn't), but because it is simple and qualitatively correct. The solution is outlined in the text, and the equations are linear, constant coefficient differential equations. After deriving the results, including initial conditions, I analyzed some properties of the solution to see if it makes sense: small viscosity and large viscosity.
