Question

The rigid bodies $A$ and $B$ of masses $2\text{kg}$ and $4\text{kg}$ respectively are rigidly connected to a spring of the constant $400\text{N/m}$. The body $B$ rests on a horizontal table, from the rest position, the body $A$ is compressed by $2\text{cm}$ and then released. Find the frequency of oscillation.

• A. $1.60\text{Hz}$
• B. $2.25\text{Hz}$
• C. $1.12\text{Hz}$
• D. $3.18\text{Hz}$

Answer 1

The correct option is B $2.25\text{Hz}$

Given,
Mass of body $A\left(m_A\right)=2\text{kg}$
Mass of body $B\left(m_B\right)=4\text{kg}$
Force constant $\left(K\right)=400\text{N/m}$
Frequency of oscillation $\left(v\right)=\frac{1}{2\pi }\sqrt{\frac{K}{m_A}}$
$=\frac{1}{2\pi }\sqrt{\frac{400}{2}}$
$=\frac{20}{2\sqrt{2}\pi }=2.25\text{Hz}$