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# hw02 - Physics 116 Homework#2 Due Friday 9/15 You may hand...

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Physics 116 Homework #2 9/07/06 Due Friday, 9/15 You may hand it in just before the lecture or immediately after the lecture. You may also hand it in earlier to your TA in your section. Read Chapter 10, including the 2 notes. 1. Background math (see Note 10.1.) (a) Write the Taylor series expansions about x = 0 for the functions e x , cos θ , and sin θ . Use the expansions to prove the Euler identity: e = cos θ + i sin θ . (b) Use the Euler identity to show that cos θ = ( e + e - ) / 2 and sin θ = ( e - e - ) / 2 i . (c) Use complex exponentials to prove the trigonometric identities : (i) cos a cos b = [cos( a + b ) + cos( a - b )] / 2 (ii) sin 2 a + cos 2 a = 1 2. Problem 10.1 3. Problem 10.2 4. Problem 10.3 5. Problem 10.5 6. A farmer named Albert is getting old and all the ruts in the field make his back hurt when he drives his tractor. He gets the idea of supporting the tractor seat with a spring instead of having it bolted to the tractor. His mass is m =75 kg and the spring compresses 1 cm when he sits in the seat.
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