What will be the force constant of the spring system shown in the figure?

A spring of force constant $k$ is cut into lengths of ratio $1:2:3$. They are connected in series and the new force constant is $k^{\text{'}}$. Then, they are connected in parallel and force constant is $k^{\text{'}\text{'}}$. Then, $k^{\text{'}}:k^{\text{'}\text{'}}$ is,

Two masses $m_1$ and $m_2$ are suspended together by a massless spring of constant $k$. When the masses are in equilibrium, $m_1$ is removed without disturbing the system. The amplitude of oscillations is,

A cylinder of mass $M$, the radius $R$ is kept on a rough horizontal plane at one extreme end of the platform at $t=0$. The axis of the cylinder is parallel to the $z$-axis. The platform is oscillating in the $xy$-plane and its displacement from the origin is represented by $x=4\cos \left(2\mathrm{\pi }t\right) \mathrm{metres}$. There is no slipping between the cylinder and the platform. Find the acceleration of the centre of mass of cylinder at $t=\frac{1}{6} \mathrm{s}$.