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Unformatted text preview: Solutions for Homework 7 3. The equations can be written like this: bracketleftbigg ˙ V ˙ I bracketrightbigg = bracketleftbigg- 1 / C 1 / L bracketrightbiggbracketleftbigg V I bracketrightbigg . Armed with Math 38 knowledge (or equivalent), you can write down the solution explicitly: V ( t ) = V ( ) cos parenleftbigg t √ LC parenrightbigg- radicalbigg L C I ( ) sin parenleftbigg t √ LC parenrightbigg , I ( t ) = I ( ) cos parenleftbigg t √ LC parenrightbigg + radicalbigg C L V ( ) sin parenleftbigg t √ LC parenrightbigg . The trajectories are ellipses. To see this, consider for instance the case I ( ) = 0. Then V ( t ) = V ( ) cos parenleftbigg t √ LC parenrightbigg , I ( t ) = radicalbigg C L V ( ) sin parenleftbigg t √ LC parenrightbigg . This describes an ellipse, with one half-axis equal to V ( ) , the other equal to radicalbig C / L × V ( ) . The second order equation for I is ¨ I =- I CL ....
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This note was uploaded on 02/28/2011 for the course MATH 150 taught by Professor Dr.borgers during the Spring '09 term at Tufts.
- Spring '09