Two springs, of force constants k_1 and k_2 , are connected to a mass m as shown (in parallel configuration).

Question

Two springs, of force constants k_1 and k_2 , are connected to a mass m as shown (in parallel configuration). The frequency of oscillation of the mass is f . If both k_1 and k_2 are made four times their original values, the frequency of oscillation becomes: ![image](https://pub-7faa453bd1ec4bf0a04c

Accepted Answer

For springs in parallel, the effective spring constant is

k_{e ff} = k_{1} + k_{2}

.The frequency is

f = \frac{1}{2 π} \frac{k _{e ff}}{m} = \frac{1}{2 π} \frac{k _{1} + k _{2}}{m}

.If

k_{1}^{'} = 4 k_{1}

and

k_{2}^{'} = 4 k_{2}

, then

k_{e ff}^{'} = 4 k_{1} + 4 k_{2} = 4 k_{e ff}

.The new frequency

f^{'}

is:

f^{'} = \frac{1}{2 π} \frac{4 k _{e ff}}{m} = 2 \times (\frac{1}{2 π} \frac{k _{e ff}}{m}) = 2 f

Two springs, of force constants $k_{1}$ and $k_{2}$ , are connected to a mass $m$ as shown (in parallel configuration). The frequency of oscillation of the mass is $f$ . If both $k_{1}$ and $k_{2}$ are made four times their original values, the frequency of oscillation becomes:

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Two springs, of force constants k1​ and k2​, are connected to a mass m as shown (in parallel configuration). The frequency of oscillation of the mass is f. If both k1​ and k2​ are made four times their original values, the frequency of oscillation becomes: