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8398631-Given second order differential equation is

1 Pages 57 views Fall'2019 29/08/2019 Mathematics 5 (1)
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Given second order differential equation is : d 2  dt 2 + g L sin = 0 where (0) =  6 ;  0 (0) = 0 This can be rewritten as: 00 (t) + g L sin = 0 -1) We use change of variables to solve this and generate two rst order equations. Let the new variables be x 1( t) and x 2( t) Let x 1( t) = (t) x 2( t) = 0 ( t) By differentiating the above two equations, we get: x 0 1 ( t) = 0 ( t) = x 2( t) x 0 2 ( t) = 00 (t) = g L sin (t) - from eqn 1 Hence, x0 2 ( t) = g L sin [x 1( t)] = 16 :085 sin[x 1( t)] —————————————————————————– To get initial conditions: x 1(0) = (0) = =6- from given information x 2(0) = 0 (0) = 0 - from given information —————————————————————————– Thus system can be written in terms of two rst order differential equations as: x 0 1 ( t) = x 2( t) , x 1(0) =  6 x 0 2 ( t) = 16 :085 sin[x 1( t)] ,x 2(0) = 0 1

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equation differential order second Given mathematics