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A body is acted upon by a force vec(F), ...

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`.

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AI Generated Solution

To find the work done by the force from time \( t = 0 \) to \( t = \frac{2\pi}{\omega} \), we will follow these steps: ### Step 1: Identify the Force and Position Vectors The force vector is given by: \[ \vec{F} = -k \left( \cos(\omega t) \hat{i} + \sin(\omega t) \hat{j} \right) \] The position vector is given by: ...
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