On a smooth inclined plane,a mass $M$ is attached between two massless springs of force constant $k$ each,as shown in the figure. The other ends of the springs are fixed to firm supports. The period of oscillation of the mass $M$ is

In the figure,$S_1$ and $S_2$ are identical springs. The oscillation frequency of the mass $m$ is $f$. If one spring is removed,the frequency will become

The scale of a spring balance which can measure from $0$ to $15 \ kg$ is $0.25 \ m$ long. If a body suspended from this balance oscillates with a time period $\frac{2 \pi}{5} \ s$,neglecting the mass of the spring,find the mass of the body suspended. (in $kg$)

$A$ particle at the end of a spring executes simple harmonic motion 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

$A$ rectangular block of mass $5\,kg$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $1\,m$ and time period $3.14\,s$. The maximum force exerted by the spring on the block is $.......N$.

An object of mass $m$ is performing simple harmonic motion on a smooth horizontal surface as shown in the figure. Just as the oscillating object reaches its extreme position,another object of mass $2m$ is placed gently on the oscillating object,and it sticks to it. Consider the following statements:
$(a)$ Amplitude of oscillation remains unchanged.
$(b)$ Time period of oscillation remains unchanged.
$(c)$ Total mechanical energy of the system does not change.
$(d)$ The maximum speed of the oscillating object changes.
Which of the above statements are correct?