Two springs of force constants K1 and K2 , respectively, 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 , respectively, 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 <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-flytdi9hgmq6.png" /> (A) f / 2 (B) f / 4 (C) 4 f (D) 2 f

Tardigrade Admin · Accepted Answer

In the given figure, two springs are connected in parallel. Therefore, the effective spring constant is given by K texteff=K1+ K2

Frequency of oscillation, textitf=(1/2 π )√(K texteff/ textitm)=(1/2 π )√(K1 + K2/ textitm) ...........(i) As K1 and K2 are increased by four times New frequency, f prime=(1/2 π) √(4(K1+K2)/m)=2 f ( using (i))

Q. Two springs of force constants $K_{1}$ and $K_{2}$ , respectively, 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

$f /2$

$f /4$

$4 f$

$2 f$

Q. Two springs of force constants K1​ and K2​ , respectively, 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

f/2

f/4

4f

2f

Q. Two springs of force constants $K_{1}$ and $K_{2}$ , respectively, 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

$f /2$

$f /4$

$4 f$

$2 f$