Find the ratio of time periods of two identical springs if they are first joined in series $\&$ then in parallel $\&$ a mass $m$ is suspended from them :

The drawing shows a top view of a frictionless horizontal surface, where there are two indentical springs with particles of mass $m_1$ and $m_2$ attached to them. Each spring has a spring constant of $1200\  N/m.$ The particles are pulled to the right and then released from the  positions shown in the drawing. How much time passes before the particles are again side by side for the first time if $m_1 = 3.0\  kg$ and $m_2 = 27 \,kg \,?$

When a particle of mass $m$ is attached to a vertical spring of spring constant $k$ and released, its motion is described by $y ( t )= y _{0} \sin ^{2} \omega t ,$ where $'y'$ is measured from the lower end of unstretched spring. Then $\omega$ is

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

A weightless spring of length $60\, cm$ and force constant $200\, N/m$ is kept straight and unstretched on a smooth horizontal table and its ends are rigidly fixed. A mass of $0.25\, kg$ is attached at the middle of the spring and is slightly displaced along the length. The time period of the oscillation of the mass is

Find the time period of mass $M$ when displaced from its equilibrium position and  then released for the system shown in figure.