Question

Two springs are connected to a block of mass $M$ placed on a frictionless surface as shown below. If both the springs have a spring constant $k$, the frequency of oscillation of block is

• A. $\frac{1}{2\pi }\sqrt{\frac{k}{M}}$
• B. $\frac{1}{2\pi }\sqrt{\frac{k}{2M}}$
• C. $\frac{1}{2\pi }\sqrt{\frac{2k}{M}}$
• D. $\frac{1}{2\pi }\sqrt{\frac{M}{k}}$

Answer 1

The correct option is B $\frac{1}{2\pi }\sqrt{\frac{k}{2M}}$

For spring block system, $n=\frac{1}{2\pi }\sqrt{\frac{k}{M}}$
Here two springs are joined in series so, total spring constant, $k_R=\frac{k_1{k}_2}{k_1+k_2}$
$k_R=\frac{k.k}{2k}=\frac{k}{2}$
So, $n=\frac{1}{2\pi }\sqrt{\frac{k}{2M}}$