Question

A block of mass $2\text{kg}$ attached to $3$ springs as shown in figure.


What is the angular frequency of oscillation if mass $m$ is slightly displaced from its equilibrium position ?
$(\text{Take,}k=100\text{N/m})$

• A. $12\text{rad/s}$
• B. $8\text{rad/s}$
• C. $5.5\text{rad/s}$
• D. $10\text{rad/s}$

Answer 1

The correct option is D $10\text{rad/s}$

Spring $1$ and $2$ are in series connection so that,

$\frac{1}{k^{\prime }}=\frac{1}{k_1}+\frac{1}{k_2}=\frac{1}{2k}+\frac{1}{2k}=\frac{1}{k}$

$\therefore k^{\prime }=k$

Now, spring $k^{\prime }$ and spring $3$ are in parallel connection with block $m$.

$\therefore k_{eq}=k^{\prime }+k_3=k+k=2k$

The angular frequency of spring block system is given by

$\omega =\sqrt{\frac{k_{eq}}{m}}=\sqrt{\frac{2k}{m}}$

$\omega =\sqrt{\frac{200}{2}}=10\text{rad/s}$

Hence, option $\left(\text{D}\right)$ is correct.