Question

The Lagrangian of a particle of mass $m$ is given by $L = \frac{1}{2}m\dot{x}^2 - \lambda x^4$, where $\lambda$ is a positive constant. If the particle oscillates with total energy $E$, then the time period of oscillations $T$ is given by:
$T = a \int_0^{\left(\frac{E}{\lambda}\right)^{\frac{1}{4}}} \frac{dx}{\sqrt{\frac{2}{m}(E - \lambda x^4)}}$
The value of $a$ is ___ (in integer).

Answer 1

The correct Answer is:4 or 4 Approx