When a body is suspended from a fixed point by a spring, the angular frequency of its vertical oscillations is $$\omega_1$$. When a different spring is used, the angular frequency is $$\omega_2$$. The angular frequency of vertical oscillations when both the springs are used together in series is given by

A

$$\omega = \left[\omega_1^2 + \omega_2^2\right]^{1/2}$$

B

$$\omega = \left[\frac{\omega_1^2 + \omega_2^2}{2}\right]^{1/2}$$

C

$$\omega = \left[\frac{\omega_1^2 \omega_2^2}{\omega_1^2 + \omega_2^2}\right]^{1/2}$$

D

$$\omega = \left[\frac{\omega_1^2 \omega_2^2}{2(\omega_1^2 + \omega_2^2)}\right]^{1/2}$$