यदि दो सरल आवर्त गतियों के विस्थापान `y_1 =10 sin [3pit +(pi)/(4)]` और ` y_2 =5 [ sin (3pit ) +sqrt3 cos (3pit) ]` है।

Explanation

`because " " y_2 =5 [sin (3pit )+ sqrt3 cos (3pit) ]` है

`therefore " " ` यदि ` " " 5- A cos phi `

और ` "5sqrt3 =A sin phi` हो

तो ` " "A =sqrt( 5^(2) +(5sqrt3)^(2) ) = 10 `

और ` " " tan phi =(5sqrt3)/( 5) = sqrt3 ` अतः ` phi =(pi)/(3) `

समीकरण (i) से

` " " y_2 -A cos phi sin ( 3pit ) +A sin phi cos ( 3pit )`

`rArr y_2 =A sin (3pi t +phi ) `

लेकिन ` " " y_2 =10 sin [3 pit +((pi)/(3))]

` अतः ` (A_1)/(A_2) =(10 )/(10 ) " " A_1 : A_2 =1:1 `

कलांतर ` =( pi)/(3) -(pi)/( 4) =(pi )/(12) `