$A$ body of mass $64 \ g$ is made to oscillate turn by turn on two different springs $A$ and $B$. Spring $A$ and $B$ have force constants $4 \ N/m$ and $16 \ N/m$ respectively. If $T_{1}$ and $T_{2}$ are the periods of oscillation of springs $A$ and $B$ respectively,then $\frac{T_{1}+T_{2}}{T_{1}-T_{2}}$ will be:

Two springs of force constants $K$ and $2K$ are connected to a mass $m$ as shown in the figure. The frequency of oscillation of the mass is:

The drawing shows a top view of a frictionless horizontal surface,where there are two identical 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 $m_2 = 27 \ kg$?

Two identical springs of spring constant $2k$ are attached to a block of mass $m$ and to fixed supports (see figure). When the mass is displaced from the equilibrium position on either side,it executes simple harmonic motion. The time period of oscillations of this system is ...... .

$A$ clock is designed based on the oscillations of a spring-block system suspended vertically in the absence of air resistance. Assume it shows the correct time when a spring of stiffness $k$ and a block of mass $m$ are used. If the block is replaced by another block of mass $4m$,choose the correct option.

Two small bodies of mass $2 \, kg$ each are attached to each other using a thread of length $10 \, cm$,and hang on a spring whose force constant is $200 \, N/m$,as shown in the figure. We burn the thread. What is the distance between the two bodies when the top body first arrives at its highest position? (Take $\pi^2 = 10$)