The drawing shows a top view of a frictionless horizontal surface, where there are two springs with particles of mass m1 and m2 attached to them. Each spring has a spring constant of 1200 N/m. The particles are pulled to the right and then released from the positions shown in the drawing. How much time passes before the particles are side by side for the first time at x = 0m if m1 = 3 kg and m2 = 27 kg. If time is \frac{nπ}{80}sec, fill n in answer.

Engineering

Physics

Constrained Relation

SHM of Spring Block System

Basics of Simple Harmonic Motion

Question

The drawing shows a top view of a frictionless horizontal surface, where there are two springs with particles of mass m₁ and m₂ attached to them. Each spring has a spring constant of 1200 N/m. The particles are pulled to the right and then released from the positions shown in the drawing. How much time passes before the particles are side by side for the first time at x = 0m if m₁ = 3 kg and m₂ = 27 kg. If time is $\frac{nπ}{80}$ sec, fill n in answer.

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$ω_{1} = \sqrt{\frac{1200}{3}} = 20$

$ω_{2} = \sqrt{\frac{1200}{27}} = \frac{20}{3}$

$ω_{1} t = (2 x + 1) \frac{π}{2}$

$ω_{2} t = (2 m + 1) \frac{π}{2} \Rightarrow \frac{3}{1} = \frac{2 n + 1}{2 m + 1}$

2n + 1 = 3

$ω_{1} t = \frac{3 π}{2} \Rightarrow t = \frac{6 π}{80}$