Important Chapters for NEET 2025 - Important Topic Physics, Chemistry & Biology

Oscillation Of Two Particle System MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

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3 Questions around this concept.

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A circular spring of natural length $l_{0}$ is cut and welded with two beads of masses is cut and welded with two beads of masses $m_{1}$ and $m_{2}$ each such that the ratio of the original spring is k then find the frequency of oscillation of the heads in a smooth horizontal rigid tube. Assume $m_{1}=m$ and $m_{2}=3 m^{\prime}$ .

$25 \sqrt{\frac{k}{3m}}$

$5 \sqrt{\frac{k}{3m}}$

$5 \sqrt{\frac{k}{m}}$

$\frac{5}{3} \sqrt{\frac{k}{m}}$

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Concepts Covered - 1

Oscillation of two particle system

Two blocks of masses $m_{1}$ and $m_{2}$ are connected with a spring of natural length l and spring constant k. The system is lying on a
frictionless horizontal surface. Initially, spring is compressed by a distance $x_{0}$ as shown in the below Figure.

If we release these blocks from the compressed position, then they will oscillate and will perform SHM about their equilibrium position.

The time period of the blocks-

In this case, the reduced mass m_ris given by $\frac{1}{m_{r}}=\frac{1}{m_{1}}+\frac{1}{m_{2}}$

and $T=2 \pi \sqrt{\frac{m_{r}}{k}}$

The amplitude of the blocks- Let the amplitude of the blocks as A₁ and A₂

$then \ \ m_{1} A_{1}=m_{2} A_{2}$

(As net external force is zero and initially the center of mass was at rest

so $\Delta x_{cm}=0 \\$ )

$\begin{array}{l} \\ {\text { By energy conservation, } \frac{1}{2} k\left(A_{1}+A_{2}\right)^{2}=\frac{1}{2} k x \frac{1}{0}} \\ {\text { or, } A_{1}+A_{2}=x_{0} \quad \text { or, } \quad A_{1}+\frac{m_{1}}{m_{2}} a A_{1}=x_{0}} \\ {\text { or, } \quad \begin{aligned} A_{1}=& \frac{m_{2} x_{0}}{m_{1}+m_{2}} \\ \text { Similarly, } & A_{2}=\frac{m_{1} x_{0}}{m_{1}+m_{2}} \end{aligned}}\end{array}$