hwsol05 2 - ME 358 Homework Solution 5 Problem 1 Derive the...

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ME 358 Homework Solution 5 Problem 1 Derive the differential equations of motion for each of the systems shown in the figure and write the formula for the circular natural frequency ω n for each system. Solution Assume y x > , y x & & > , 0 x > & a) ( ) ( ) [ ] m k ky kx x m y x k x m 0 F n = ω = + + = = & & & & b)
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( ) ( ) ( ) m k F kx x c x m F kx x c x m 0 F n = ω = + + + + + = = & & & & & & c) ( ) ( ) ( ) ( ) ( ) m k k 0 x k k x c x m x k x k x c x m 0 F 2 1 n 2 1 2 1 + = ω = + + + + + + = = & & & & & & & d)
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( ) ( ) ( ) [ ] ( ) m k k y k x k k x m y x k x k x m 0 F 2 1 n 2 2 1 2 1 + = ω = + + + + = = & & & & e) ( ) ( ) [ ] ( ) m k y c kx x c x m kx y x c x m 0 F n = ω = + + + + = = & & & & & & & & f)
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