B$.6$ For the shown system, drive the differential equation of motion for the

cylinder that has a mass of $10xkg$ and calculate the natural frequency

of vertical oscillation of the spring$-$loaded cylinder when it is set into

motion. Both springs are in tension at all times and have $k=50y\frac{N}{m}.$

If the cylinder is released from equilibrium position with velocity $0\mathrm{.}4$

$\frac{m}{s},$ determine the equation which describes its motion. If the

amplitude of the cylinder's steady$-$state vibration is $4\mathrm{.}2cm,$ determine

the wheel's angular velocity $.$ Note that have $c=12y$ N$.$s $\frac{?}{m},r=6$

$cm.$