A mass $\backslash ($ m $\backslash )$ is placed at the tip of a cantilever beam with a length $\backslash ($ L $\backslash ),$ elastic modulus E$,$ and moment of inertia I. At the point where the mass is placed, the beam is also supported by a spring with a spring constant k and a damping element with a damping coefficient c$.$ From the vibration data taken from the mass, it is observed that the vibration amplitude decreases to $\backslash (1/7\backslash )$ of its initial value after $6$ periods. Find the spring constant kkk of the added spring, neglecting the mass of the cantilever beam.