Question

In the reported figure, two bodies \(A\) and \(B\) of masses \(200~\text {gms}\) and \(800~\text {gms}\) are attached with the system of springs. Springs are kept in a stretched position with some extension, when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be \(\text{rad/s}\) when \(k = 20~ \text {N/m}\)

• A. 10.0
• B. 10

Answer 1

Answer: (A), (B)

$\omega =\sqrt{\frac{k_{eq}}{\mu }}$
$\mu =$ reduced mass

Here, the springs are joined in series.
$k_{eq}=\frac{k_1{k}_2}{k_1+k_2}$

$=\frac{k\times 4k}{5k}=\frac{4k}{5}$

$=\frac{4\times 20}{5}=16\text{N/m}$

$\mu =\frac{m_1{m}_2}{m_1+m_2}=\frac{0.2\times 0.8}{0.2+0.8}=0.16\text{kg}$

$\omega =\sqrt{\frac{16}{0.16}}=\sqrt{100}=10\text{rad/s}$