A potential is given by $V\left(x\right)=\frac{k(x+a{)}^2}{2}$ for $x<0$ and $V\left(x\right)=\frac{k(x-a{)}^2}{2}$ for $x>0$. The schematic variation of oscillation period $T$ for a particle performing periodic motion in this potential as a function of its energy $E$ is:

Total energy of a particle performing S.H.M. is NOT proportional to

A mass of $5 \mathrm{kg}$ is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length $4 \mathrm{m}$ has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed ?

A body of mass $1 \mathrm{kg}$ is executing simple harmonic motion. Its displacement $y\left(\mathrm{cm}\right)$ at $t$ seconds is given by $y=6\sin \left(100t+\frac{\pi }{4}\right)$. Its maximum kinetic energy is

An object of mass $4 \mathrm{kg}$ is attached to a spring which is fixed at one end on a rigid support and the mass-spring system is kept on a frictionless table. The object is allowed to execute simple harmonic motion along $X$ - direction. The force constant of the spring is $10 \mathrm{N} {\mathrm{m}}^{-1}$ and the spring is stretched initially a distance of $5 \mathrm{cm}$, the total energy stored in the system is