Two springs, of force constants 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

Question

Two springs, of force constants 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 (A) 2 f (B) f/2 (C) f/4 (D) 4 f

Tardigrade Admin · Accepted Answer

Step-(i) Calculation of frequency, when spring constant Changes
Since, As a given - spring constant of both springs are made four times their original value
So

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

k_{2} = 4 k_{2}

Now

k^{'} = k_{1}^{'} + k_{2}^{'} = 4 k_{1} + 4 k_{2}

k^{'} = 4 (k_{1} + k_{2})

Now frequency is given as -

f^{'} = \frac{1}{2 n} \frac{k ^{'}}{m} = \frac{1}{2 π} \frac{4 ( k _{1} + k _{2} )}{m}

f^{'} = 2 (\frac{1}{2 n} \frac{k _{1} + k _{2}}{m})

...(ii)
from eq (i) & (ii)

f^{'} = 2 f

Q. Two springs, of force constants 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

2 f

f/2

f/4

4 f

Q. Two springs, of force constants $k_{1}$ 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