Circular Motion

A particle moves along an arc of a circle of radius $$R$$ according to the law $$l=a\sin{\omega t}$$, where $$l$$ is the displacement from the initial position measured along the arc, and $$a$$ and $$\omega$$ are constants. Assume $$R=1.00\:m$$, $$a=0.80\:m$$, and $$\omega=2.00\:rad/s^2$$.
If the system shown in the figure is rotated in a horizontal circle with angular velocity $$\displaystyle \omega:\left ( g= 10m/s^{2} \right )$$
If the system shown in the figure is rotated in a horizontal circle with angular velocity $$\displaystyle \omega:\left ( g= 10m/s^{2} \right )$$
In a uniform circular motion - 
A string can withstand a tension of $$25\ N$$. What is the greatest speed at which a body of mass $$1\ kg$$ can be whirled in a horizontal circle using $$1\ m$$ length of the string?