Rev2 - 1 REVISION (2) Version 1 At y = 10π ⇒ t = 2π...

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Unformatted text preview: 1 REVISION (2) Version 1 At y = 10π ⇒ t = 2π sec, x=10m At y=25 (π/2) ⇒ t=5(π/2) sec, x=0 At y=30(π/2) ⇒ t=3π sec, x=-10m At y=35(π/2) ⇒ t=7(π/2) sec, x=0 At y=20 π ⇒ t=4π sec, x=10m The path is periodic it repeats itself every 2π sec. Answer the following question: The curvilinear motion of a particle is described by the relations : t sin 10 x y , x x + = − = & & & & & . The particle starts from the position (A) where 5 y , x , y , 10 x , t A A A A = = = = = & & . Determine the Cartesian equation and the parametric equations . Plot the path and prove that the motion on the path is periodic and determine the periodic time The coordinates are in meters and the time in seconds. ( ) ( ) ( ) y , s / m 5 y , t cos 10 x , t sin 10 x ) 7 ........( .......... 5 y cos 10 x ) 3 ( in 5 y t ) 6 .......( .......... .......... .......... .......... .......... t 5 y ) 5 .( .......... .......... .......... .......... .......... s / m 5 y ) 4 ....( t sin 10 t sin 10 t sin 10 x y ) 3 ....( t cos 10 x 2 t 10 x sin 1 sin 10 x sin t x 100 dx dt dt dx x ) 2 .....( x 100 x x 100 x 2 100 2 x 2 x xdx x d x ) 1 ...( x x .. . .. . . . .. 1 1 1 x 10 2 t . 2 . 2 2 . 2 2 . x 10 x . . .. . = = − = − =       = ⇒ = = = = + − = + = = ⇒       + ± =       ⇒       −       = ± ⇒ − ± = ⇒ = − ± = ⇒ − = ⇒         − − = ⇒ − = − = − − − ∫ ∫ ∫ ∫ π x y -10 10 2 5 π 2 10 π 2 15 π 2 20 π 10m/s 2 10m/s 2 10m/s 2 5m/s 5m/s 5m/s 2 REVISION (2) Version 2 Answer the following question: The curvilinear motion of a particle is described by the relations : y y , x x − = − = & & & & . The particle starts from the position (A) where : y x , 2 y x , t A A A A = = − = = = & & . Determine the parametric equations and the Cartesian equation. Plot the path and prove that the motion on the path is oscillating about axix y − and determine the period of oscillation. The coordinates are in meters and the time in seconds. ( ) ( ) ( ) ( ) " 1 slope " line Straight ) 7 ...( x y ) 6 .........( .......... .......... .......... t cos 2 y ) 2 ( 2 y sin t y 4 dy dt dt dy y ) 5 .....( y 4 y ydy y d y ) 4 .( .......... .......... .......... .......... .......... y y ) 3 ........( .......... .......... .......... t cos 2 x ) 2 ( 2 x sin t x 4 dx dt dt dx x ) 2 .....( x 4 x x 4 x 2 4 2 x 2 x xdx x d x ) 1 ....( x x 1 y 2 2 t . 2 . y 2 y . . .. 1 x 2 2 t . 2 . 2 2 . 2 2 . x 2 x . . .. . . = − = − = ⇒       − −       = ± ⇒ − ± = ⇒ = − ± = ⇒ − = − = − = ⇒       − −       = ± ⇒ − ± = ⇒ = − ± = ⇒ − = ⇒       − − = ⇒ − = − = − − − − − − ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ π π . sec 2 period B & A btw n Oscillatio A c s / m 2 y x & y x m 2 y x sec, 2 t s / m 2 y x & y x...
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This note was uploaded on 12/21/2010 for the course ENGINEERIN mp108 taught by Professor Elbarki during the Spring '08 term at Alexandria University.

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Rev2 - 1 REVISION (2) Version 1 At y = 10π ⇒ t = 2π...

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