Question

Find the natural frequency of oscillation of spring block system shown.

• A. $\frac{7}{\pi }\text{Hz}$
• B. $\frac{10}{\pi }\text{Hz}$
• C. $\frac{3}{\pi }\text{Hz}$
• D. $\frac{5}{\pi }\text{Hz}$

Answer 1

The correct option is B $\frac{10}{\pi }\text{Hz}$

Given:
$m=1\text{kg};k=200\text{N/m}$

We know that for spring-block system, time period,

$T=2\pi \sqrt{\frac{m}{k_{\text{net}}}}$

Here, springs is in parallel.

$k_{\text{net}}=k_1+k_2=2k$

$\therefore T=2\pi \sqrt{\frac{m}{2k}}$

So,
$f=\frac{1}{T}=\frac{1}{2\pi }\sqrt{\frac{2k}{m}}$

$\Rightarrow f=\frac{1}{2\pi }\sqrt{\frac{2\times 200}{1}}$

$\Rightarrow f=\frac{10}{\pi }\text{Hz}$

Hence, option $\left(b\right)$ is the correct answer.

$\begin{array}{c}\text{Why this question ?}\\ \text{Concept - For a spring-block system, whether the system is kept horizontal,}\\ \text{vertical or inclined, the time period remain the same.}\\ \text{Only amplitude of the SHM varies.}\end{array}$