PROBLEM 5 & 6 April 2 2010

PROBLEM 5 & 6 April 2 2010 - damping. The top...

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SOLVING PROBLEM 5 April 2, 2010 (like 12.31): A 1 kg ball on a spring (with spring constant k = 1 N/m) oscillates up and down in air which provides a damping force v b R with b = 0.01 N s m -1 . The initial total energy is 1 J. After what time has the total energy fallen by the factor 1/e? What do you know? The amplitude damping rate is b /2 m = 0.005 s -1 . The energy damping rate is double this (0.01 s -1 ). The energy as a function of time is } 01 . 0 exp{ } ) / ( exp{ 0 0 t E t m b E E Thus the time for the energy to decrease by a factor of 1/e is 100 s. SOLVING PROBLEM 6 (like 12.36): A 1 kg ball on a spring (with spring constant k = 1 N/m) oscillates up and down with negligible
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Unformatted text preview: damping. The top support of the spring oscillates up and down with peak-to-peak amplitude 0.01m at angular frequency 1.1 s-1 . What is the equilibrium peak-to-peak amplitude of the oscillation of the ball? What do you know? The perturbing displacement is amplified by half the ratio of the resonant angular frequency to the angular frequency difference . The resonant angular frequency is 1 s-1 . The angular frequency difference is 0.1 s-1 . Half the ratio of them is 5. Thus the equilibrium peak-to-peak amplitude is 0.01 m x 5 = 0.05 m....
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