Two spring block systems are shown in figure. If in both cases, the amplitude of oscillation of each of the blocks is same, then

Engineering

Physics

Center of Mass

Basics of Simple Harmonic Motion

SHM of Spring Block System

Question

Two spring block systems are shown in figure. If in both cases, the amplitude of oscillation of each of the blocks is same, then

4(Max. K.E_A) = (Max. K.E_B)

Max. v_A > Max. v_B

f_A : f_B = 2 : 1

T_A : T_B = 1

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$E_{B} = \frac{1}{2} \times 2 m \times \frac{k}{2 m} A^{2}$

$E_{A} = \frac{1}{2} \times m \times \frac{k}{m / 2} \times A^{2} \times 2 = 2 {kA}^{2}$

$f_{A} = \sqrt{\frac{2 k}{m}} f_{B} = \sqrt{\frac{k}{2 m}}$

$\frac{f_{A}}{f_{B}} = 2 : 1$

$v_{A} = {Aω}_{A} = A \sqrt{\frac{2 k}{m}}$

$v_{B} = {Aω}_{B} = A \sqrt{\frac{k}{2 m}}$