Two masses $m_1$ and $m_2$ connected by a spring of spring constant $k$ rest on a frictionless surface. If the masses are pulled apart and let go, the time period of oscillation is

Springs of spring constants $K, 2K, 4K, 8K,$ ….. are connected in series. A mass $40\, gm$ is attached to the lower end of last spring and the system is allowed to vibrate. What is the time period of oscillation ….. $\sec$. (Given $K = 2\, N/cm$)

A spring balance has a scale that reads from $0$ to $50\; kg$. The length of the scale is $20\; cm .$ A body suspended from this balance, when displaced and released, oscillates with a period of $0.6\; s$. What is the weight of the body in $N$?

On a smooth inclined plane, a body of mass $M$ is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant $K$, the period of oscillation of the body (assuming the springs as massless) is

Two masses $M_{A}$ and $M_{B}$ are hung from two strings of length $l_{A}$ and $l_{B}$ respectively. They are executing SHM with frequency relation $f_{A}=2 f_{B}$, then relation