Question

A linearly elastic beam of length 2l with flexural rigidity EI has negligible mass. A massless spring with a spring constant k and a rigid block of mass m are attached to the beam as shown in the figure.

The natural frequency of this system is

• A. $\sqrt{\frac{kl^3+6EI}{ml^3}}$
• B. $\sqrt{\frac{kl^3+48EI}{ml^3}}$
• C. $\sqrt{\frac{6EIk}{(kl^3+6EI)m}}$
• D. $\sqrt{\frac{48EIk}{(kl^3+48EI)m}}$

Answer 1

Answer: (A)

$\sqrt{\frac{kl^3+6EI}{ml^3}}$

Answer 2

The correct option is (A) : $\sqrt{\frac{kl^3+6EI}{ml^3}}$.