The differential equation, obtained on eliminating A and B from the equations `y= A cos omega wt+ B sin omega t` is

Options

A. `y_(2)=- omega^(2)y`
B. `y_(1)+y=0`
C. `y_(2)+y_(1)=0`
D. `y_(1)-omega^(2)y=0`

Answer

A

Explanation

Given, ` y = A cos omega t+ B sin omega t`
On differentiting w.r.t.t we get
`(dy)/(dt)=-A omega sin omega t + B omega cos omega t` ltbr On again differentiating, we get,
`(d^(2)y)/(dt^(2))=- A omega cos omega t- B omega^(2) sin omega t`
`=- omega^(2)(A cos omega t+ B sin omega t)`
`=- omega^(2) y`
`rArr y_(2) =- omega^(2) y`
Which is required differentail equation,