D 2 n2 I D kI g t 2 g t t 2 t 2 g t t 2 t 3 2 x n2 x g t n r n r n r n n x n2 x g t f t f t f t u t a t a f t 0 t 0 f t t t 0 f t 0 t 0 f t 1 t t 0 f t 0 t 0 f t 2t 1 0 t 1 f t 0 t 1 f t 0 t 0 f t t t t 0 t t w 2D 2 4D 4I v v w u p D 2u t u t t u t t2 q t cos t w t q t w t D kI x kx q t q t 1 w t q t w t D2 n2 I x n2 x q t t2 t t t2 t t t t t t t 0 w e kt v 1 k 1 e kt w 1 n sin n t v 1 n2 1 cos n t MIT OpenCourseWare http ocw mit edu 18 03 Differential Equations Spring 2010 For information about citing these materials or our Terms of Use visit http ocw mit edu terms
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