solution_for_HW3 - Solution of HW3 Phys 310 00 Intermediate...

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Solution of HW3 – Phys 310 00 Intermediate Mechanics Fall 2011 SHO – Simple Harmonic Oscillations Problem #1 15 points a. According to picture. ʌ spring constant: 22 2 2 2 11 2 0 . 5* 4 88 m N T k m k gs m kT SS S §· ± ¨¸ ©¹ 2 * N k k m b. 0 1 ( ) c o s () 4 221 42 0.4 x t At T s T Am ZI Z ² ³ 0 s in ( ) dx v t x t dt Z ZI ²³ ± To determine 0 I we need to use initial conditions. According to picture x(0)=0 at equilibrium position 0 00 (0) cos( *0 ) 0 *0 xA ³ ± ³ ± Then 1 ( ) 0.4cos( ) 1 ( ) 0 . 2 s i n x tt v ³ c. Disagree. This formula 0 S v t works only in case of constant velocity. In case of oscillations 0 v is not constant. Energy conservation law helps us to determine 0 v : 2 2 0 0.125 0.4 0.2 2 2 0.5 v k A k Ak m m v vA s mm 0 0.2 m v s
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Problem #2 20 points a. b. Net force on the bob that points tangent to the path of the bob = sin mg I Yes, this force and angle displacement always have opposite signs. No. If we write second Newton’s law for bob we will see. 22 ( ) sin x m x y mg mg xy ± ² ² ± ±± ( )0 x x yg l ± It not looks like equation of simple harmonic motion.
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This note was uploaded on 12/07/2011 for the course PHYS 310 taught by Professor Jones,m during the Fall '08 term at Purdue University-West Lafayette.

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solution_for_HW3 - Solution of HW3 Phys 310 00 Intermediate...

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