Question

What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants are denoted by $k_{1}and{k}_2$ as shown below

• A. $\sqrt{\frac{k_1+k_2}{2m}}$
• B. $\sqrt{\frac{k_1+k_2}{4m}}$
• C. $\sqrt{\frac{k_1-k_2}{m}}$
• D. $\sqrt{\frac{k_1+k_2}{m}}$

Answer 1

The correct option is D $\sqrt{\frac{k_1+k_2}{m}}$

$m\ddot{x}+(k_1+k_2)x=0$

$\ddot{x}+\left(\frac{k_1+k_2}{m}\right)x=0$

$\therefore$ ${\omega }_n=\sqrt{\frac{k_1+k_2}{m}}$