In the given figure,a body of mass $M$ is held between two massless springs on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has a spring constant $k,$ the frequency of oscillation of the given body is:

In the following questions,match Column-$I$ with Column-$II$ and choose the correct options.

$A$ block of mass $M$ hangs from a spring and oscillates vertically with an angular frequency $\omega$. If the block is removed from the spring,when it is in equilibrium position,the spring shortens by

On a frictionless horizontal plane,a bob of mass $m=0.1 \text{ kg}$ is attached to a spring with natural length $l_0=0.1 \text{ m}$. The spring constant is $k_1=0.009 \text{ N/m}$ when the length of the spring $l > l_0$ and is $k_2=0.016 \text{ N/m}$ when $l < l_0$. Initially,the bob is released from $l=0.15 \text{ m}$. Assume that Hooke's law remains valid throughout the motion. If the time period of the full oscillation is $T=(n \pi) \text{ s}$,then the integer closest to $n$ is:

Two springs of spring constants $k_1$ and $k_2$ are connected to a mass $m$ as shown in the figure. Under negligible friction, if the mass is displaced by a small amount $x$ from its equilibrium position and released, the period of oscillation is

If a body of mass $0.98\, kg$ is made to oscillate on a spring of force constant $4.84\, N/m$,the angular frequency of the body is ..... $rad/s$. (in $.22$)