Graphical Mechanics(Part 4)

Two rings each of mass mm are connected with a spring of stiffness kk and natural length ll as shown. Rings are constrained to move along wedge\text{wedge} shaped y=1x\displaystyle y = \frac{1}{|x|}. The system is released from rest\text{rest}. Find its Time Period TT in seconds\text{seconds}.

Enter answer as 20T20T.

Details and Assumptions

  • All surfaces are smooth\color{#3D99F6}{\text{smooth}}

  • Take acceleration due to gravity g=10m/s2\color{#3D99F6}{g = 10m/s^2}

  • Spring is ideal\color{#3D99F6}{\text{ideal}} and has natural length l=2m\color{#3D99F6}{l = 2m}

  • Stiffness of spring k=2mg N/m\color{#3D99F6}{k = 2mg \text{ N/m}}

  • Initially, rings are at (0.5,2)\color{#3D99F6}{(-0.5, 2)} and (0.5,2)\color{#3D99F6}{(0.5, 2)} respectively.

Inspiration Aniket Sanghi

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