A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of platform. Now the platform is given an angular velocity ${\mathrm{\omega }}_0.$ When the tortoise moves along the chord of the platform with a constant velocity (with respect to the platform); The angular velocity of platform $\mathrm{\omega }\left(\mathrm{t}\right)$ will vary with time $‘\mathrm{t}’$ as