A body is acted upon by a force `vec(F)`, given by
`vec(F)=-k[(cos omega t)hat(i)+(sin omega t) hat(i)]` undergoes displacement, where the position vector
`vec(r)` of the body is given by `vec(r)=a[cos ( omega t+ alpha) hat(i)+ sin ( omega t+ alpha) hat(j)]`. Find the work done by the force from time `t=0` to time `t=2pi//omega`.

Explanation

To solve the problem, we need to find the work done by the force \(\vec{F}\) on a body as it moves from time \(t=0\) to \(t=\frac{2\pi}{\omega}\). The force and position vector are given as follows:

\[ \vec{F} = -k \left( \cos(\omega t) \hat{i} + \sin(\omega t) \hat{j} \right) \]

\[
\vec{r} = a \left( \cos(\omega t + \alpha) \hat{i} + \sin(\omega t + \alpha) \hat{j} \right)
...