The drawing shows a top view of a frictionless horizontal surface, where there are two indentical 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 again side by side for the first time if m1 = 3.0 kg and m2 = 27 kg ?

Engineering

Physics

Constrained Relation

Basics of Simple Harmonic Motion

Calculus

Question

The drawing shows a top view of a frictionless horizontal surface, where there are two indentical 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 again side by side for the first time if m₁ = 3.0 kg and m₂ = 27 kg ?

$\frac{π}{20} \sec$

$\frac{π}{10} \sec$

$\frac{π}{40} \sec$

$\frac{3 π}{40} \sec$

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$w_{1} = \sqrt{\frac{k}{m_{1}}} = \sqrt{\frac{1200}{3}} = 20 rad / s$

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

$π - θ = \frac{20}{3} t$

π + θ = 20t

$2 π = (20 + \frac{20}{3}) t$

$t = \frac{6 π}{80} = \frac{3 π}{40} \sec$