Μεθοδολογια Μηχανικες ταλαντωσεις
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Transcript of Μεθοδολογια Μηχανικες ταλαντωσεις
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1 (.. ...)
1 . t=0 x=? u=?: x u . (x=0 )2 t=0 . = + => = +(x,u t=0)3 t=0 x=A ( + ) u=A ( + ) .: ( = ) t=0 x=0 u>0: ... F = = - Kx . ... D=K .
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1 (.. ...)
1 . t=0 x=? u=?: x u . (x=0 )2 t=0 . = + => = +(x,u t=0)3 t=0 x=A ( + ) u=A ( + ) .: ( = ) t=0 x=0 u>0: ... F = = - Kx . ... D=K .
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1 (.. ...)
1 . t=0 x=? u=?: x u . (x=0 )2 t=0 . = + => = +(x,u t=0)3 t=0 x=A ( + ) u=A ( + ) .: ( = ) t=0 x=0 u>0: ... F = = - Kx . ... D=K .
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2 (.. ...)1 .
2 ( ) F = 0 => = mg => K = mg => = mg/K3 . t=0 x=? u=?: x u . (x=0 )4 t=0 . = + => = + (x,u t=0)5 t=0 x=A ( + ) u=A ( + ) .: ( = ) t=0 x=0 u>0: ... ( x ) F = mg - = mg K( + ) = mg- K -Kx = -Kx ... D=( 2 K = mg )!!!
= K l (l ..) = x (x )
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( ) = ( ) = - 2
2 (.. ...)1 .
2 ( ) F = 0 => = mg => K = mg => = mg/K3 . t=0 x=? u=?: x u . (x=0 )4 t=0 . = + => = + (x,u t=0)5 t=0 x=A ( + ) u=A ( + ) .: ( = ) t=0 x=0 u>0: ... ( x ) F = mg - = mg K( + ) = mg- K -Kx = -Kx ... D=( 2 K = mg )!!!
= K l (l ..) = x (x )
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( ) = ( ) = - 2
2 (.. ...)1 .
2 ( ) F = 0 => = mg => K = mg => = mg/K3 . t=0 x=? u=?: x u . (x=0 )4 t=0 . = + => = + (x,u t=0)5 t=0 x=A ( + ) u=A ( + ) .: ( = ) t=0 x=0 u>0: ... ( x ) F = mg - = mg K( + ) = mg- K -Kx = -Kx ... D=( 2 K = mg )!!!
= K l (l ..) = x (x )
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( ) = ( ) =
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3 (.. ...)
1 . ( )2 ( ) F = 0 => = mg => K = mg => = mg /K3 . t=0 x=? u=?: x u . (x=0 )4 t=0 . = + => = +(x,u t=0)5 t=0 x=A ( + ) u=A ( + ) .: ( = ) t=0 x=0 u>0: ... ( x ) F = mg - = mg K( + ) = mg - K -Kx = -Kx ... D=( 2 K = mg )!!!
= K l (l ..) = x (x )
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3 (.. ...)
1 . ( )2 ( ) F = 0 => = mg => K = mg => = mg /K3 . t=0 x=? u=?: x u . (x=0 )4 t=0 . = + => = +(x,u t=0)5 t=0 x=A ( + ) u=A ( + ) .: ( = ) t=0 x=0 u>0: ... ( x ) F = mg - = mg K( + ) = mg - K -Kx = -Kx ... D=( 2 K = mg )!!!
= K l (l ..) = x (x )
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3 (.. ...)
1 . ( )2 ( ) F = 0 => = mg => K = mg => = mg /K3 . t=0 x=? u=?: x u . (x=0 )4 t=0 . = + => = +(x,u t=0)5 t=0 x=A ( + ) u=A ( + ) .: ( = ) t=0 x=0 u>0: ... ( x ) F = mg - = mg K( + ) = mg - K -Kx = -Kx ... D=( 2 K = mg )!!!
= K l (l ..) = x (x )
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: ( ) = ( ) =: (mg) (mg )
: () .
= W , W . : mgh (+ )4 ( ) . .
. x . ( ) .: .
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: ( ) = ( ) =: (mg) (mg )
: () .
= W , W . : mgh (+ )4 ( ) . .
. x . ( ) .: .
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: ( ) = ( ) =: (mg) (mg )
: () .
= W , W . : mgh (+ )4 ( ) . .
. x . ( ) .: .
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5 ( ) ( ) ( ) . (1 )
: x .(2 )!!!! . 1 , . 1 : m + ( = )
6 ( )1 ( ) ( ) . (1 )2 : , X1 X2 .!!! ( ) .
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5 ( ) ( ) ( ) . (1 )
: x .(2 )!!!! . 1 , . 1 : m + ( = )
6 ( )1 ( ) ( ) . (1 )2 : , X1 X2 .!!! ( ) .
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5 ( ) ( ) ( ) . (1 )
: x .(2 )!!!! . 1 , . 1 : m + ( = )
6 ( )1 ( ) ( ) . (1 )2 : , X1 X2 .!!! ( ) .
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3 F=0 X1 X2 : F = 0 => = mg => K = g => = g/K F = 0 => = ( + )g => K = ( + )g => = ( + )g/K
4 x (2 )!!! : t=0 x= x2 x1 u =
5 t=0 . = + => = ( + ) + ( 2 )6 t=0 x=A ( + ) u=A ( + ) .: ( = ) t=0 x=0 u>0: ... ( x F = mg - = ( + )g K( + ) = ( + )g- K -Kx = -Kx ... D=* 3 K = ( + )g**: =
7 ( )* ( 6) mg mg X1 X2 .** (3 )
X1 X2
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3 F=0 X1 X2 : F = 0 => = mg => K = g => = g/K F = 0 => = ( + )g => K = ( + )g => = ( + )g/K
4 x (2 )!!! : t=0 x= x2 x1 u =
5 t=0 . = + => = ( + ) + ( 2 )6 t=0 x=A ( + ) u=A ( + ) .: ( = ) t=0 x=0 u>0: ... ( x F = mg - = ( + )g K( + ) = ( + )g- K -Kx = -Kx ... D=* 3 K = ( + )g**: =
7 ( )* ( 6) mg mg X1 X2 .** (3 )
X1 X2
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3 F=0 X1 X2 : F = 0 => = mg => K = g => = g/K F = 0 => = ( + )g => K = ( + )g => = ( + )g/K
4 x (2 )!!! : t=0 x= x2 x1 u =
5 t=0 . = + => = ( + ) + ( 2 )6 t=0 x=A ( + ) u=A ( + ) .: ( = ) t=0 x=0 u>0: ... ( x F = mg - = ( + )g K( + ) = ( + )g- K -Kx = -Kx ... D=* 3 K = ( + )g**: =
7 ( )* ( 6) mg mg X1 X2 .** (3 )
X1 X2
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8 ( )
1 2 1 . 2 d :1 1 2. 1 ( ) . 2 2 = = =d ( =d)
: 1 A1 (1= ). 2 : umax = umax1 => d = 1 19 ( - )
(N) m. ( +m )1 (1 ) (2 ). d : t=0 x=d u=0. t=0 . ( =d)
2 =
m D1 = m2 => D1 = m
m F1 = - D1 x = -m x .(x 2 )3 m F1 = N mg
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8 ( )
1 2 1 . 2 d :1 1 2. 1 ( ) . 2 2 = = =d ( =d)
: 1 A1 (1= ). 2 : umax = umax1 => d = 1 19 ( - )
(N) m. ( +m )1 (1 ) (2 ). d : t=0 x=d u=0. t=0 . ( =d)
2 =
m D1 = m2 => D1 = m
m F1 = - D1 x = -m x .(x 2 )3 m F1 = N mg
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8 ( )
1 2 1 . 2 d :1 1 2. 1 ( ) . 2 2 = = =d ( =d)
: 1 A1 (1= ). 2 : umax = umax1 => d = 1 19 ( - )
(N) m. ( +m )1 (1 ) (2 ). d : t=0 x=d u=0. t=0 . ( =d)
2 =
m D1 = m2 => D1 = m
m F1 = - D1 x = -m x .(x 2 )3 m F1 = N mg
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4 2 F1 N:N mg = -m x => N = mg - m x
!!! 0 . mg - m x 0 => x ( ) .
*!!! ( m+M)g (m+M)g . . . .9 ( - )
.1 (1 ) (2 ). d : t=0 x=d u=0. t=0 . ( =d)2 F=0 . , ( )!!! F x F=0 => N+F-m2g=0 => N= m2g-F => = m2g- x( F=Kx , x )3 0 => m2g- x 0 => x
x = !!
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4 2 F1 N:N mg = -m x => N = mg - m x
!!! 0 . mg - m x 0 => x ( ) .
*!!! ( m+M)g (m+M)g . . . .9 ( - )
.1 (1 ) (2 ). d : t=0 x=d u=0. t=0 . ( =d)2 F=0 . , ( )!!! F x F=0 => N+F-m2g=0 => N= m2g-F => = m2g- x( F=Kx , x )3 0 => m2g- x 0 => x
x = !!
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4 2 F1 N:N mg = -m x => N = mg - m x
!!! 0 . mg - m x 0 => x ( ) .
*!!! ( m+M)g (m+M)g . . . .9 ( - )
.1 (1 ) (2 ). d : t=0 x=d u=0. t=0 . ( =d)2 F=0 . , ( )!!! F x F=0 => N+F-m2g=0 => N= m2g-F => = m2g- x( F=Kx , x )3 0 => m2g- x 0 => x
x = !!
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2 K = 1+ 2 . F = + = - K1 x K2 x = - (K1 + K2 ) x
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2 K = 1+ 2 . F = + = - K1 x K2 x = - (K1 + K2 ) x
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2 K = 1+ 2 . F = + = - K1 x K2 x = - (K1 + K2 ) x