10 using the newtons second law model for a vibrating

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10. Using the Newton’s second law model for a vibrating mass-spring system with damping and no forcing, my ' ' + b y ' + ky = 0 , find the equation of motion if m = 10 kg, b = 40 kg/sec, k = 240 kg/sec 2 , y ( 0 )= 1.0 , and y ' ( 0 ) = 0.0 m/sec. 10 y '' + 40 y ' + 240 y = 0 simplify y '' + 4 y ' + 24 y = 0 auxiliary equation r 2 + 4 r + 24 = 0 r = 4 ± ( 4 2 ) 4 ( 1 )( 24 ) 2 ( 1 ) 4 ± 16 96 2 4 ± 80 2 2 ± 2 i 5 r= 2 + 2 i 5 r= 2 2 i 5

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