Answer:
Explanation:
The general equation for the disk with moment of inertia I when given small angular displacement [tex]\theta [/tex] is given by
[tex]I\frac{\mathrm{d^2} \theta }{\mathrm{d} t^2}=-k\theta[/tex]
[tex]\frac{\mathrm{d^2} \theta }{\mathrm{d} t^2}+\frac{k\theta }{I}=0[/tex]
Replacing
[tex]\frac{k\theta }{I}=\omega ^2[/tex]
where [tex]\omega[/tex] is the angular frequency of oscillation
General solution for this Equation is given by
[tex]\theta =\theta _{max}\sin \left ( \omega t+\phi \right )[/tex]
where [tex]\theta _{max}=maximum\ angular\ displacement[/tex]
[tex]\phi =Phase\ difference[/tex]
Thus K can be written as
[tex]k=I\omega ^2[/tex]
