When a mass ' $m$ ' is connected individually to the springs $s_1$ and $s_2$, the oscillation frequencies…

When a mass ' $m$ ' is connected individually to the springs $s_1$ and $s_2$, the oscillation frequencies are $v_1$ and $v_2$. If the same mass is attached to the two springs as shown in the figure, the oscillation frequency would be

  1. $v_1+v_2$
  2. $\sqrt{v_1^2+v_2^2}$
  3. $\left(\frac{1}{v_1}+\frac{1}{v_2}\right)^{-1}$
  4. $\sqrt{v_1^2-v_2^2}$

Solution

$\begin{aligned} & \text { } \delta_1=\sqrt{\frac{\mathrm{S}_1}{\mathrm{~m}}}, \delta_2=\sqrt{\frac{\mathrm{S}_2}{\mathrm{~m}}} \\ & \delta=\sqrt{\frac{\mathrm{S}_{\mathrm{eq}}}{\mathrm{m}}}=\sqrt{\frac{\mathrm{S}_1+\mathrm{S}_2}{\mathrm{~m}}}=\sqrt{\frac{\mathrm{m} \delta_1^2+\mathrm{m} \delta_2^2}{\mathrm{~m}}} \\ & \therefore \delta=\sqrt{\mathrm{v}_1^2+\mathrm{v}_2^2}\end{aligned}$

Asked in: AP EAMCET 2024 (22 May Shift 1)

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