A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. [2023]

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Solution

Q.
A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is $\frac{π}{\sqrt{x}}$ in SI unit. The value of $x$ is ________. [2023]

Ans.
(5)

$F = - 2 k x, a = - \frac{2 k x}{m},$

$ω = \sqrt{\frac{2 k}{m}} = \sqrt{\frac{2 \times 20}{2}} = \sqrt{20} rad/s$

$T = \frac{2 π}{ω} = \frac{2 π}{\sqrt{10}} = \frac{π}{\sqrt{5}} \Rightarrow x = 5$

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