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Two masses m1\text m_1m1​​ and m2\text m_2m2​​ are connected by a massless spring of spring constant k. The system is free to oscillate alon
Question

Two masses m1\text m_1​ and m2\text m_2 are connected by a massless spring of spring constant k. The system is free to oscillate along the length of spring. The system oscillates with a frequency:

A.

12πkμ where μ=((m1 m2)/(m1+m))\frac{1}{2 \pi} \sqrt{\frac{k}{\mu}} \text { where } \mu=\left(\left(\mathrm{m}_1 \mathrm{~m}_2\right) /\left(\mathrm{m}_1+\mathrm{m}\right)\right)​​

B.

μk where μ=((m1 m2)/(m1+m2))\sqrt{\frac{\mu}{k}} \text { where } \mu=\left(\left(\mathrm{m}_1 \mathrm{~m}_2\right) /\left(\mathrm{m}_1+\mathrm{m}_2\right)\right)​​

C.

kμ where μ=((m1 m2)/(m1+m2))\sqrt{\frac{k}{\mu}} \text { where } \mu=\left(\left(\mathrm{m}_1 \mathrm{~m}_2\right) /\left(\mathrm{m}_1+\mathrm{m}_2\right)\right)​​

D.

12πμk where μ=((m1 m2)/(m1+m2))\frac{1}{2 \pi} \sqrt{\frac{\mu}{k}} \text { where } \mu=\left(\left(\mathrm{m}_1 \mathrm{~m}_2\right) /\left(\mathrm{m}_1+\mathrm{m}_2\right)\right)​​

Correct option is A

For two masses m1 and m2 connected by a massless spring with spring constant k, the system will oscillate with a frequency. The frequency f of oscillation of the two-mass system is given by:\text{For two masses } m_1 \text{ and } m_2 \text{ connected by a massless spring with spring constant } k, \text{ the system will oscillate with a frequency. The frequency } f \text{ of oscillation of the two-mass system is given by:}f=12πkμf = \dfrac{1}{2\pi} \sqrt{\dfrac{k}{\mu}}

Where:μ is the reduced mass of the system.\text{Where:}\\\begin{aligned}\mu &\text{ is the reduced mass of the system.}\end{aligned}

μ=m1m2m1+m2\mu = \dfrac{m_1 m_2}{m_1 + m_2}

f=12πkm1m2m1+m2f=12πkμ where μ=m1m2m1+m2f = \dfrac{1}{2\pi} \sqrt{\dfrac{k}{\dfrac{m_1 m_2}{m_1 + m_2}}}\\f = \dfrac{1}{2\pi} \sqrt{\dfrac{k}{\mu}} \text{ where } \mu = \dfrac{m_1 m_2}{m_1 + m_2}​​​​​

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