Frequency of oscillation of a body is 5 Hz when a force F _ 1 is...

According to the question,

${F}_{1} = - {k}_{1}x$ and ${F}_{2} = - {k}_{2}x$

$∴$ Frequency of oscillation

${v}_{1} = \dfrac{1}{2\pi}\sqrt{\dfrac{k1}{m}}$

$5 = \dfrac{1}{2\pi}\sqrt{\dfrac{k1}{m}}$

$⇒ {k}_{1} = 100{\pi}^{2}m$

Similarly, $12 = \dfrac{1}{2\pi}\sqrt{\dfrac{k2}{m}}$

$⇒ {k}_{2} = 576{\pi}^{2}m$

Now, $F = {F}_{1} + {F}_{2} = - \left({k}_{1} + {k}_{2}\right)x$

$∴$ Frequency of oscillation,

$v = \dfrac{1}{2\pi}\sqrt{\dfrac{{k}_{1} + {k}_{2}}{m}} = \dfrac{1}{2\pi}\sqrt{\dfrac{100{\pi}^{2}m + 576{\pi}^{2}m}{m}}$

$⇒ v = 13Hz$