The oscillation of a body on a smooth horizontal surface is represented by the equation, X=Acos (omega t) where X= displacement at time t omega = frequency of oscillation. Which one of the following graph shows correctly the variation a with ?

The oscillation of a body on a smooth horizontal surface is represente

1.	The oscillation of a body on a smooth horizontal surface is represented by the equation, X=Acos (omega t) where X= displacement at time t omega = frequency of oscillation. Which one of the following graph shows correctly the variation a with ?
Answer» Solution :Here `x=A COS omega t` `:.` VELOCITY `v=(DX)/(dt)=(d)/(dt)(A cos omegat)` `=-A omega sin omega t` Acceleration, `=a(DV)/(d)/(dt)(-A omega sin omegat)` `=-A omega^(2) cos ^(2) omega t :. A prop cos omega ` Hence the variation of a with t is correctly shown by graph (d).