Two springs are connected to a block of mass M placed on a frictionless surface as shown below. If both the springs have a spring constant k,, the frequency of oscillation of the block is :

Two springs are connected to a block of mass M placed on a frictionless surface as shown below. If both the springs have a spring constant k,, the frequency of oscillation of the block is :

A
$\frac{1}{2 π} \sqrt{\frac{k}{M}}$
B
$\frac{1}{2 π} \sqrt{\frac{k}{2 M}}$
C
$\frac{1}{2 π} \sqrt{\frac{2 k}{M}}$
D
$\frac{1}{2 π} \sqrt{\frac{M}{k}}$

Solution:

$k_{eff} = \frac{k \times k}{k + k} = \frac{k}{2}, f = \frac{1}{2 π} \sqrt{\frac{k_{eff}}{M}} = \frac{1}{2 π} \sqrt{\frac{k}{2 M}}$

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