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

SHM of Spring Block System

Basics of Simple Harmonic Motion

Center of Mass

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

T_A : T_B = 1

f_A : f_B = 2 : 1

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

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

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

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

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

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