KE & PE Graph

Q. A body is in motion along the positive $x$ - axis, according to the relation $x=a{\sin }^2\omega t$. Then, the variation of its kinetic energy $K$ with time $t$ may be represented by

1. 
2. 
3. 
4. 

Q.

A particle free to move along the x-axis has potential energy given by $U\left(x\right)=k(1-e^{-x^2})$ For $-\infty <x<\infty$, where k is a positive constant of appropriate dimensions. Then

1. At points away from the origin, the particle is in unstable equilibrium

2. For any finite non-zero value of x, there is a force directed away from the origin

3. If its total mechanical energy is U, it has its minimum kinetic energy at the origin

4. For small displacements from x = 0, the motion is simple harmonic

Q. A body executes simple harmonic motion. The potential energy $\left(PE\right)$, the kinetic energy $\left(KE\right)$ and total energy $\left(TE\right)$ are measured as a function of displacement $\left(x\right)$. Which of the following statements is true?

1. $PE$ is maximum when $x=0$
2. $KE$ is maximum when $x=0$
3. $TE$ is zero when $x=0$
4. $KE$ is maximum when $x$ is maximum