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Damped Oscillations

Two springs, ...

Question

Two springs, of force constant $k_{1}$ and $k_{2}$ , are connected to a mass m as shown. 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

f / 2

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f / 4

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4 f

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2 f

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Solution

The correct option is D $2 f$
This system can be treated as two parallel spring system with spring constants $k_{1}$ and $k_{2}$ . Now, frequency
$f = \frac{1}{2 π} \sqrt{\frac{k_{1} + k_{2}}{m}}$
When both $k_{1}$ and $k_{2}$ are made four times their original value, the new frequency becomes:
$f^{'} = \frac{1}{2 π} \sqrt{\frac{4 k_{1} + 4 k_{2}}{m}}$
$= \frac{1}{2 π} 2 \sqrt{\frac{k_{1} + k_{2}}{m}}$
$= 2 f$

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Two springs, of force constant k1 and k2, are connected to a mass m as shown. 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

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