The time period of the given spring-mass system is:

Two identical springs of spring constant $k$ are attached to a block of mass $m$ and to fixed supports as shown in the figure. When the mass is displaced from its equilibrium position on either side, it executes a simple harmonic motion. The period of oscillations is:

      

1. $2 \pi \sqrt{\dfrac{{m}}{4{k}}}$
2. $2 \pi \sqrt{\dfrac{2{m}}{{k}}}$
3. $2 \pi \sqrt{\dfrac{{m}}{2{k}}}$
4. $2 \pi \sqrt{\dfrac{{m}}{{k}}}$

When a mass $m$ is connected individually to two springs $S_1$ and $S_2,$ the oscillation frequencies are $\nu_1$ and $\nu_2.$ If the same mass is attached to the two springs as shown in the figure, the oscillation frequency would be: 

A spring having a spring constant of $1200$ N/m is mounted on a horizontal table as shown in the figure. A mass of $3$ kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of $2.0$ cm and released. The maximum acceleration of the mass is: