{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Final-SP07

# Final-SP07 - Phys 208 Theoretical Physics Final exam 8i...

This preview shows pages 1–2. Sign up to view the full content.

Phys 208 – Theoretical Physics – Final exam – May 10, 2007 1.(15 pts) a) Find and plot the roots of 3 8 i . b) Evaluate ( ) i i in Cartesian form, i.e. , x iy + form. c) Determine the points in the ( x, y ) plane that satisfy the equation | 2 3 | 4 z i + = . 2.(20 pts) Find the exponential Fourier transform of the given function ( ) f x and write ( ) f x as a Fourier integral [that is, find ( ) g α and substitute your result into the integral for ( ) f x ]. 1, 1 0 ( ) 1, 0 1 0, | | 1 x f x x x < < = < < > a) Show that you obtain 0 cos 1 sin( ) ( ) 2 x d f x α π α α α = and list the possible results of the integral that you can obtain depending on the value of x . b) Using Parseval’s theorem for Fourier transforms , what would be the result for the integral given by 2 2 0 (cos 1) d α α α Recall Parseval’s theorem is 2 2 1 | ( ) | | ( ) | 2 g d f x dx α α π −∞ −∞ = 3.(15 pts) A ball of mass M and radius R rolls without slipping down an inclined plane under the action of gravity.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern