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Assignmen t 1 solution - PHYS-232 Heat and Waves Homework 1...

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Unformatted text preview: PHYS-232 Heat and Waves - Homework 1 Winter Semester 2008 Due on Thursday, January 24, 2008 1. Solve problem 1.2.1 of the class notes. Answer: With the extra weight m 2 , the new balance point should be x = m 2 g/k . The angular frequency of the oscillation should be radicalBig k/ ( m 1 + m 2 ). The oscillation start at x = 0, and balanced at x = A = m 2 g/k . Therefore the function describing the resulting oscillation should be: x = m 2 g k − m 2 g k cos( radicalBigg k m 1 + m 2 t ) (1) 2. Solve problem 1.2.5 of the class notes. Answer: V ( x ) = V [( a x ) 12 − 2( a x ) 6 ] (2) V ′ ( x ) = 12 V a [( a x ) 7 − ( a x ) 13 ] (3) Let V ′ ( x ) = 0, we can find the balance point x = a . V ′′ ( x ) = 12 V a [ 13 a ( a x ) 14 − 7 a ( a x ) 8 ] (4) The angular frequency of the small oscillation about the balance point is ω = radicalBig V ′′ ( a ) m = radicalBig 72 V a 2 m = 6 radicalBig 2 V a 2 m ....
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This note was uploaded on 04/29/2008 for the course PHYS 232 taught by Professor Vinals during the Winter '08 term at McGill.

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Assignmen t 1 solution - PHYS-232 Heat and Waves Homework 1...

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