Question

In the figure all springs are identical having spring constant k and mass m each. The block also has mass m. The frequency of oscillation of the block is:

Answer 1

spring constant = k, mass = m

The frequency of oscillation of the block is,

$\Rightarrow f=\frac{1}{2\pi }\sqrt{\frac{k_{eq}}{m_{eq}}}$

Here,

m = mass of the block

$M_{spring}=$ mass of the spring.

Since all the springs are in parallel. So,

$M_{spring}=3mand{k}_{eq}=3k$.

$m=m+\frac{M_{spring}}{3}$

$\Rightarrow f=\frac{1}{2\pi }\sqrt{\frac{k_{eq}}{m_{eq}}}$

$f=\frac{1}{2\pi }\sqrt{\frac{k_{eq}}{m+\frac{M_{spring}}{3}}}$

$f=\frac{1}{2\pi }\sqrt{\frac{3k}{m+\frac{3m}{3}}}$

$\Rightarrow f=\frac{1}{2\pi }\sqrt{\frac{3k}{2m}}$

Final answer: (b)