Question

The potential energy of a particle oscillating on x-axis is $U=20+(x-2{)}^2$. Here U is in joules and x in meters. Total mechanical energy of the particle is 36 J.
a)State whether the motion of the particle is simple harmonic or not.
b)Find the mean position.
c)Find the maximum kinetic energy of the particle.

Answer 1

Total energy given at Extreme position of oscillation evenrope in purele potential energy of maximum $u$

$36=20+(x-2{)}^2$

$(x-2{)}^2=16x-2=\pm 4$

$\therefore x=+6$ and $-2$

The Two values o $x$ provides the txtream position of $x$ at which potential energy in maximum

$\therefore \frac{6-2}{2}=2$ (mean position)