Two identical springs, each of force constant k are connected I `(a)` series `(b)` parallel and they support a mass M. Calculate the ratio of the frequency of oscillation of the mass in two systems.

Options

A. `1 :1`
B. `1 : 2`
C. `2 : 1`
D. `4 : 1`

Answer

C

Explanation

When they are joined in series, the effective force constant is `(K//2)` and when they are joined in parallel, the force constant is 2K.
`omega =sqrt((K)/(m)) therefore(2pi)/(T)= sqrt((K)/(m)) therefore T=2pi sqrt((m)/(K))`
`therefore (T_(1))/(T_(2))=(2pi)/(2pi) sqrt((m)/(K//2)xx(2K)/(m))=sqrt(4)=2`
`therefore T_(1)=2 T_(2)`