Two springs, of force constants `k_(1)` and commected to a mass (m) as shown. The frequency of oscillation of the mass is (f). If both `K_(2) are made four times their original values, the frequency of oscillation becomes .

Options

A. (a) `2f`
B. (b) `f//2`
C. (c )`f//4`
D. (d) `4f`

Answer

A

Explanation

(a) The two springs are in parallel.
`f=1/2_(pi)sqrtK_(1)+k_(2)/m`
`f'=1/2_(pi)sqrt(4K_(1)+4K^(2))/m`
`1/2_(pi)sqrt((4(K_91)+4K_(2)))/m=2(1/2(pi)sqrt(K_(1)+K_(2))/m`
`=2f`.