# Two springs, of force constants and are connected to a mass as shown. The frequency of oscillation of the mass is .      If both and are made four times their original values, the frequency of oscillation becomes Option 1) Option 2) Option 3) Option 4)

Answers (1)

As we learnt in

Parallel combination of spring -

- wherein

are spring constants of spring 1 & 2 respectively.

In the given figure two springs are connected in parallel. Therefore the effective spring constan is given by

$k_{eff}= k_{1}+k_{2}$

Frequency of oscillation,

$f= \frac{1}{2\pi }\sqrt{\frac{k_{eff}}{m}}= \frac{1}{2\pi }\sqrt{\frac{k_{1}+k_{2}}{m}}\cdots \cdots \cdots \cdots (i)$

As    $k_{1}$   and   $k_{1}$   are increased four times N ew frequency,

${f}'= \frac{1}{2\pi }\sqrt{\frac{4\left ( k_{1}+k_{2} \right )}{m}}= 2f\: \: \: (Using (i))$

Correct option is 1.

Option 1)

This is the correct option.

Option 2)

This is an incorrect option.

Option 3)

This is an incorrect option.

Option 4)

This is an incorrect option.

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