The cantilever beam as shown In figure below is made up of m

The cantilever beam, as shown In figure below is made up of mild steel. It has negligible weight and is carrying a mass M at its free end and it also resting an elastic support of stiffness K_1 as shown. If K_2 represents the bending stiffness of the beam, the natural frequency for the system will be a. Squareroot K_1^2 K_2^2/M(K_1 + K_2) b. Squareroot K_1 + K_2/2M c. Squareroot (K_1 + K_2)^2/M d. Squareroot K_1 + K_2/M

Solution

The two springs are connected in parallel, that is the beam (k1) and helical spring (k2)

The helical spring will deflect by the same amount as that of beam. Therefore the springs are in

Parallel. If the spring is connected above the mass then springs will be in series.

Therefore The equivalent stiffness of given figure= Keq= K1+K2

Therefore natural frequency= square root of ((K1+K2)/m)