The potential energy of a particle of mass $0.02 \ kg$ moving along the $x$-axis is given by $V = A x(x-4) \ J$,where $x$ is in metres and $A$ is a constant. Which of the following is/are correct statement$(s)$?

The mass $M$ shown in the figure oscillates in simple harmonic motion with amplitude $A$. The amplitude of the point $P$ is

Four massless springs whose force constants are $2K, 2K, K$ and $2K$ respectively are attached to a mass $M$ kept on a frictionless plane as shown in the figure. If mass $M$ is displaced in the horizontal direction,then the frequency of the oscillating system is:

$A$ mass $M$ is suspended from a light spring. An additional mass $m$ added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period

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:

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 $kg$)