What is time constant in LC circuit?
An LC circuit never settles, so there is no transient period and 'time constant' does not apply. 

For a standard 2nd order TF with damping (e.g. resistance), time constant is usually approximated by: \$\tau\approx\large\frac{1}{\zeta\omega_n}\$, but this measure doesn't have a lot of relevance if \$ \small\zeta&lt;1\$.

In the case of a series RLC circuit, for example, \$\small\zeta=\frac{R}{2}\sqrt{\frac{C}{L}}\$, and \$\omega_n=\frac{1}{\sqrt{LC}}\$, giving \$\tau=\frac{2L}{R}\$.