HW1 09F solution

# HW1 09F solution - 1 2 aLj j H H vb v o o = 1 1 2 aLj j H H...

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ME 487 Assignment 1 1. Given j v b aLj E L - = Derive A j v b A L a R L 2 - = proof: j v b aLj E L - = J=I/A I vA b A I aL E L - = Divide by I and Multiply last term by A/A 2 2 I vA b A aL E L - = A j v b A L a R L 2 - =

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2. Given L a o H H H + = Derive ) ( 1 L o vH j H v + = φ Proof: L a o H H H + = v j H a φ = So L a H v j H + = φ Multiply by v and divide by H o o L o H vH H j v + = φ Pull out 1/H o ) ( 1 L o vH j H v + = φ
3. Given ) ( 1 L o vH j H v + = φ Derive ) ( 1 2 aLj j b H v o + + = φ Proof: b v Lj a H L + = 2 substitute in ]) [ ( 1 2 b v Lj a v j H v o + + = φ
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Unformatted text preview: ) ( 1 2 aLj j H H vb v o o + = + ) ( 1 ) 1 ( 2 aLj j H H b v o o + = + ) ( ) 1 ( 1 2 aLj j H b H v o o + + = Simplify again ) ( 1 2 aLj j b H v o + + =...
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