Two springs of force constants 2k and k are c | vedclass

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(D) When a mass $m$ is connected between two springs with force constants $k_1$ and $k_2$ in parallel, the effective spring constant $k_{eff}$ is give

Vedclass · Accepted Answer

$\frac{1}{2\pi} \sqrt{\frac{3k}{m}}$

Vedclass · Answer

(D) When a mass $m$ is connected between two springs with force constants $k_1$ and $k_2$ in parallel, the effective spring constant $k_{eff}$ is given by $k_{eff} = k_1 + k_2$.In this problem, the two springs are connected in parallel to the mass $m$. Therefore, the effective spring constant is $k_{eff} = 2k + k = 3k$.The frequency of oscillation $f$ for a spring-mass system is given by the formula $f = \frac{1}{2\pi} \sqrt{\frac{k_{eff}}{m}}$.Substituting the value of $k_{eff}$, we get $f = \frac{1}{2\pi} \sqrt{\frac{3k}{m}}$.Thus, the correct option is $D$.

Two springs of force constants $2k$ and $k$ are connected to a mass $m$ as shown. The mass is displaced slightly to one side and released. The frequency of oscillation of the two springs-mass system is

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