In the adjacent figure,if the inclined plane is smooth and the springs are identical,then the period of oscillation of this body is

$A$ mass $m$ is suspended from a spring of length $l$ and force constant $K$. The frequency of vibration of the mass is $f_1$. The spring is cut into two equal parts and the same mass is suspended from one of the parts. The new frequency of vibration of the mass is $f_2$. Which of the following relations between the frequencies is correct?

If two similar springs each of spring constant $K$ are joined in series,the new spring constant and time period would be changed by a factor of:

$A$ body at the end of a spring executes $S.H.M.$ with a period $t_1$,while the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $T$,then

As shown in the figure, a block of weight $20 \,N$ is connected to the top of a smooth inclined plane by a massless spring of constant $8 \pi^2 \,Nm^{-1}$. If the block is pulled slightly from its mean position and released, the period of oscillations is (Acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,s$)

$A$ body of mass $M$ and charge $q$ is connected to a spring of spring constant $k$. It is oscillating along the $x-$ direction about its equilibrium position,taken to be at $x = 0$,with an amplitude $A$. An electric field $E$ is applied along the $x-$ direction. Which of the following statements is correct?