HW01 - Phys. 315, Spring 2012 Homework #1 Due: Weds., Jan...

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Phys. 315, Spring 2012 Homework #1 Due: Weds., Jan 25, start of class. 1. (10 points) French, problem 1-1. Do this problem by working with the real and imaginary parts a, b, c, and d of 12 and . zz You may find the following trigonometric sum relation helpful: ± ² ± ² ± ² ± ² ± ² tan tan tan 1t a n t a n DE ³ ³ ´ (CRC Standard Mathematical Tables, 31 st edition, section 6.1.11 ) 2. (6 points) Find the magnitude A and the phase angle I of the vectors 1 23 , zi ³ and ± ² 2 2 ´ in the complex plane. 3. (8 points) French, problem 1-8. 4. (14 points) Simple Harmonic Oscillator equation . The equation that describes the oscillation of a mass m suspended by a spring of spring constant k is 2 2 0, d mk dt [ where is the displacement of the mass from its equilibrium position. a) Verify that ± ² ( ) cos tA t [Z ³ is a solution of this equation if and only if k m Z . b) Suppose that you know that ± ² ( ) cos t ³ for some definite values of A and .
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HW01 - Phys. 315, Spring 2012 Homework #1 Due: Weds., Jan...

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