Mathematic Methods HW Solutions 47

Mathematic Methods HW Solutions 47 - Chapter 9 47 5.5 L = 1...

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Unformatted text preview: Chapter 9 47 5.5 L = 1 2 m x 2- 1 2 kx 2 m x + kx = 0 5.6 L = 1 2 m ( r 2 2 + r 2 sin 2 2 )- mgr cos braceleftBigg a - a sin cos 2- g sin = 0 ( d/dt )(sin 2 ) = 0 5.8 L = 1 2 m (2 r 2 + r 2 2 )- mgr 2 r- r 2 + g = 0 ( d/dt )( r 2 ) = 0 5.9 L = 1 2 m (2 r 2 + r 2 2 )- mgr 2 r- r 2 + g = 0 r 2 = const. 5.10 L = 1 2 m 1 (4 r 2 + r 2 2 ) + 2 m 2 r 2- m 1 gr 3 + m 2 g ( l- 2 r ) 4( m 1 + m 2 ) r- m 1 r 2 + m 1 g 3 + 2 m 2 g = 0 r 2 = const. 5.11 L = 1 2 ( m + Ia- 2 ) z 2- mgz (If z is taken as positive down, ( ma 2 + I ) z + mga 2 = 0 change the signs of z and z .) 5.12 L = 1 2 m ( r 2 + r 2 2 )- bracketleftbig 1 2 k ( r- r ) 2- mgr cos bracketrightbig r- r 2 + k m ( r- r )- g cos = 0, d dt ( r 2 ) + gr sin = 0 5.13 L = 1 2 m [ r 2 (1 + 4 r 2 ) + r 2 2 ]- mgr 2 r (1 + 4 r 2 ) + 4 r r 2- r 2 + 2 gr = 0, r...
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