First slide

Simple hormonic motion

Question

Four massless springs whose force constants are 2k, 2k, k and 2 k respectively are attached to a mass M kept on a frictionless plane (as shown in figure). If the mass M is displaced in the horizontal direction, then the frequency of the system.

Moderate

A

$\frac{1}{2 π} \sqrt{\frac{k}{4 M}}$
B

$\frac{1}{2 π} \sqrt{\frac{4 k}{M}}$
C

$\frac{1}{2 π} \sqrt{\frac{k}{7 M}}$
D

$\frac{1}{2 π} \sqrt{\frac{7 k}{M}}$

Solution

Effective K = $\frac{1}{k_{s}} = \frac{1}{2 k} + \frac{1}{2 k} k_{s} = k$
$k_{p} = k + 2 k = 3 k$
3k and k are parallel
$\begin{array}{l} k_{(e f f)} = 4 k \\ n = \frac{1}{2 π} \sqrt{\frac{4 k}{m}} \end{array}$

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