Question

Two point masses of $3\text{kg}$ and $6\text{kg}$ are attached to opposite ends of a horizontal spring, whose spring constant is $300{\text{Nm}}^{-1}$, as shown in the figure. The natural vibration frequency of the system is, approximately,

• A. $4\text{Hz}$
• B. $3\text{Hz}$
• C. $2\text{Hz}$
• D. $1\text{Hz}$

Answer 1

The correct option is C $2\text{Hz}$

Given,
$m_1=3\text{kg},m_2=6\text{kg}$

Spring constant $\left(K\right)=300\text{N/m}$

Reduced mass of two blocks is,

$\left(\mu \right)=\frac{m_1{m}_2}{m_1+m_2}$

$=\frac{3\times 6}{9}=2\text{kg}$

Now, frequency of the system is given by,

$f=\frac{1}{2\pi }\sqrt{\frac{K}{\mu }}$

$=\frac{1}{2\pi }\sqrt{\frac{300}{2}}\approx 2\text{Hz}$

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