Page 6 - Vibrations
P. 6
The acceleration at the displacement x is given by,
2
+ = 0
2
To solve this differential equation, use the D operator,
2
( + ) = 0
or
1/2 1/2
( + [ ] ) ( − [ ] ) = 0
= + −
= √
Express this as,
= cos( + )
where
2
2
= √ + and = tan −1 ( )
The velocity,
= − sin( + )
5
