The homogeneous disk is vertically suspended by a wire, with a spring on one side. The disk has a radius of $1$ m and a mass $m=10kg.$ The spring constant is $10\frac{N}{m}.$ The disk is initially stationary in its equilibrium position. If a downward force $F(t)=10cos(8t)N$ is applied, what is the equation of the motion of the centre of the disk? Determine the position of the centre of the disk as a function of time.

Ans: $x(t)=-0\mathrm{.}003289cos(16\mathrm{.}33t)+0\mathrm{.}003289cos(8t)$

Question $7$