hw3 - Homework 3 PHZ 3113 Due Friday, January 29, 2010...

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Homework 3 PHZ 3113 Due Friday, January 29, 2010 Chapter 2-3 1. Find z = cos - 1 ( i 8) in the form x + iy (Some of this problem was done in class) 2. We showed in class that for the simple harmonic oscillator, described the equation of motion, d 2 y dt + ω 2 0 y = 0 the we could take the solution to be y ( t ) = A cos( ω 0 t ) + B sin( ω 0 t ) or y ( t ) = Ce 0 t , with A and B real and C complex, and the actual displacement in the second case given by Re [ y ( t )] = Re [ Ce 0 t ]. The values of A and B or C can be found if we know the y ( t = 0) and ± dy dt ² t =0 . Writing C = C ( r ) + iC ( i ) , find an expression for C ( r ) and C ( i ) in terms of the A and B . Finally, assume we know the initial conditions, y ( t = 0) = y 0 and ± dy dt ² t =0 = v 0 . Find expressions for A and B , and also C , in terms of y 0 . v 0 , and ω 0 . 3. In class, we found the particular solution y ( t ) to the damped, driven simple harmonic oscillator, described by, d 2 y dt 2 + 2 b dy dt + ω 2 0 y = F D cos( ωt ) We also showed that this was
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hw3 - Homework 3 PHZ 3113 Due Friday, January 29, 2010...

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