First slide

Applications of SHM

Question

In arrangement given in figure, if the block of mass m is displaced, the frequency is given by

Moderate

A

$n = \frac{1}{2 π} \sqrt{(\frac{k_{1} - k_{2}}{m})}$
B

$n = \frac{1}{2 π} \sqrt{(\frac{k_{1} + k_{2}}{m})}$
C

$n = \frac{1}{2 π} \sqrt{(\frac{m}{k_{1} + k_{2}})}$
D

$n = \frac{1}{2 π} \sqrt{(\frac{m}{k_{1} - k_{2}})}$

Solution

With respect to the block the springs are connected in parallel combination.
$∴$ Combined stiffness k = k₁+ k₂ and $n = \frac{1}{2 π} \sqrt{\frac{k_{1} + k_{2}}{m}}$

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