A point mass oscillates along the x-axis according to the law, `x=x_(0)cos(omegat-pi/4)`. If the acceleration of the particle is written as `alpha=Acos(omegat+delta)`, find A and `delta`.

Explanation

`x=x_(0)\cos(omegat-pi/4)`
`therefore` Velocity, `v=(dx)/(dt)=-omegax_(0)sin(omegat-pi/4)`
and acceleration, `alpha=(dv)/(dt)=-omega^(2)x_(0)cos(omegat-pi/4)`
`=+omega^(2)x_(0)cos(omegat-pi/4+pi)`
`=omega^(2)x_(0)cos(omegat+(3pi)/4)`
Given `alpha=Acos(omegat+delta)`
So comparing the two equations we have, `A=omega^(2)x_(0)anddelta=(3pi)/4`.