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solution_for_HW3

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. period: 4 ʌ spring constant: 2 2 2 2 2 1 1 2 0.5 * 4 8 8 m N T k m kg s m k T S S S S § · § · ¨ ¸ ¨ ¸ © ¹ © ¹ 2 1 1 * 8 8 N k kg s m b. 0 1 ( ) cos( ) 4 2 2 1 4 2 0.4 x t A t T s T A m Z I S S S Z S ± ² 0 ( ) ( ) sin( ) dx v t x t A t dt Z Z I ± ² ± To determine 0 I we need to use initial conditions. According to picture x(0)=0 at equilibrium position 0 0 0 (0) cos( *0 ) 0 *0 2 2 x A S S Z I Z I I ² ² Then 1 ( ) 0.4cos( ) 2 2 1 ( ) 0.2sin( ) 2 2 x t t v t t S S ² ± ² 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 2 2 0 0 0 0.125 0.4 0.2 2 2 0.5 v kA kA k m m v v A s m m 0 0.2 m v s
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