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Q.

Two blocks each of mass m is connected to the spring of spring constant k as shown in the figure.
If the blocks are displaced slightly in opposite directions and released, they will execute simple harmonic motion. The time period of oscillation is

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a

$2 π \sqrt{\frac{m}{k}}$

b

$2 π \sqrt{\frac{m}{2 k}}$

c

$2 π \sqrt{\frac{m}{4 k}}$

d

$2 π \sqrt{\frac{2 m}{k}}$

answer is B.

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Detailed Solution

Reduced mass of the system

$μ = \frac{(m) (m)}{m + m} = \frac{m}{2}$

$∴$ Time period, $T = 2 π \sqrt{\frac{μ}{k}} = 2 π \sqrt{\frac{m}{2 k}}$

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Two blocks each of mass m is connected to the spring of spring constant k as shown in the figure. If the blocks are displaced slightly in opposite directions and released, they will execute simple harmonic motion. The time period of oscillation is