A particle is moving on x-axis has potential energy $\mathrm{U}=2-20\mathrm{x}+5{\mathrm{x}}^2$J along x-axis. The particle is released at x = - 3. The maximum value of 'x' is _________.

[x is in meters and U is in joule]

Given that $\mathrm{U}=2-20\mathrm{x}+5{\mathrm{x}}^2$

Interaction force on particle is given as

$\mathrm{F}=-\frac{\mathrm{dU}}{\mathrm{dx}}=20-10\mathrm{x}$

As F is linearly varying with -x, particle is executing SHM
At equilibrium position F = 0

$\Rightarrow 20-10\mathrm{x}=0\Rightarrow \mathrm{x}=2$

Since particle is released at x = - 3, therefore amplitude of particle is 5.

It will oscillate about x = 2 with an amplitude of 5.
$\Rightarrow$ Maximum value of x will be 7.