Question

The natural frequency (rad/sec) of the system shown in figure. below is.

• A. $\sqrt{\frac{K}{m}}$
• B. $\sqrt{\frac{2K}{m}}$
• C. $\sqrt{\frac{K}{2m}}$
• D. $\sqrt{\frac{4K}{m}}$

Answer 1

The correct option is A $\sqrt{\frac{K}{m}}$

$\text{The springs are inclined to the direction of oscillation. The equivalent stiffness of the inclined spring is K}{\cos }^2\alpha \text{the two inclined springs are parallel. The equivalent stiffness is}2K{\cos }^2{45}^{\circ }=K\text{and natural frequency is}\sqrt{\frac{K}{m}}\text{rad/sec}$