1. Tardigrade
  2. Question
  3. Physics
  4. The potential energy of a particle executing SHM is given by V ( x )=(1/2) kx 2 where k is force constant. For k =0.5 N / m the graph of PE as a function of x is shown below. Find the position of particle having total energy 1 J moving in this potential at which it must turn back to its original position.

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Q. The potential energy of a particle executing $SHM$ is given by $V ( x )=\frac{1}{2} \,kx ^{2}$ where $k$ is force constant. For $k =0.5 \,N / m$ the graph of $PE$ as a function of $x$ is shown below. Find the position of particle having total energy $1 \,J$ moving in this potential at which it must turn back to its original position.Physics Question Image

Solution:

Particle turns back when
$KE =0$ and $PE = TE =1 J$
$\frac{1}{2} kx ^{2}=\frac{1}{2} \times 0.5 x ^{2}=1$
$x^{2}=4$ or $x=\pm 2 \,m$