The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The maximum speed of junction P is V0. Assume springs are massless. Select the correct option/s

Engineering

Physics

Center of Mass

Basics of Simple Harmonic Motion

SHM of Spring Block System

Question

The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The maximum speed of junction P is V₀. Assume springs are massless. Select the correct option/s

Amplitude of potential energy in springs S₁ and S₂ is respectively $\frac{1}{9}$ kA₂ and kA₂

$V_{0} = A \sqrt{\frac{8 k}{27 M}}$

$V_{0} = A \sqrt{\frac{8 k}{81 M}}$

Amplitude of potential energy in springs S₁ and S₂ is respectively $\frac{2}{9}$ kA₂ and $\frac{1}{9}$ kA₂

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$\frac{2 k}{3} A = {kS}_{p}$

${Sp}_{1} = \frac{2}{3} A$

${Sp}_{2} = \frac{A}{3}$

$U_{1 max} = \frac{1}{2} k \times \frac{4 A^{2}}{9} = \frac{2 {kA}^{2}}{9}$

$U_{2 max} = \frac{1}{2} 2 k \times \frac{A^{2}}{9} = \frac{{kA}^{2}}{9}$

$V_{0} = \frac{2 A}{3} \times \sqrt{\frac{2 k}{3 m}}$