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mws_ind_ode_txt_euler_Examples

mws_ind_ode_txt_euler_Examples - Chapter 08.02 Eulers...

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08.02.1 Chapter 08.02 Euler’s Method for Ordinary Differential Equations- More Examples Industrial Engineering Example 1 The open loop response, that is, the speed of the motor to a voltage input of 20 V, assuming a system without damping is w dt dw ) 06 . 0 ( (0.02) 20 . If the initial speed is zero   0 0 w , and using Euler’s method, what is the speed at s 8 . 0 t ? Assume a step size of s 4 . 0 h . Solution w dt dw 3 1000 w w t f 3 1000 , The Euler’s method reduces to h w , t f w w i i i i 1 For 0 i , 0 0 t , 0 0 w h w , t f w w 0 0 0 1 4 0 0 0 0 . , f   4 . 0 0 3 1000 0 4 0 1000 0 . rad/s 400 1 w is the approximate speed of the motor at h t t t 0 1 4 . 0 0 s 4 . 0 400 4 . 0 1 w w rad/s For 1 i , 4 . 0 1 t s, 400 1 w h w , t f w w 1 1 1 2 4 . 0 400 , 4 . 0 00 . 400 f 4 0 400 3 1000 00 400 . . 4 . 0 200 400 rad/s 320
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08.02.2 Chapter 08.02 2 w
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