In the figure given below, a block of mass M = 490 g placed on a frictionless table is connected with two springs having same spring constant (K = 2 N m⁻¹). If the block is horizontally displaced through ' X ' m then the number of complete oscillations it will make in 14π seconds will be _____________. Numerical answer type. Work it out, then open the answer.

Answer: 20. Both springs push back on the block: keff = 2K = 4 N/m. T = 2π√(0.49/4) = 2π(0.35) = 0.7π s Number of oscillations = (14π)/(0.7π) = 20

In the figure given below, a block of mass M = 490 g placed on a… | JEE Main 2023 (31 Jan, Shift 1)

Q56JEE Main 2023 · 31 JAN · SHIFT 1Medium

Spring Systems

In the figure given below, a block of mass $M = 490\text{ g}$ placed on a frictionless table is connected with two springs having same spring constant $\left(K = 2\text{ N m}^{-1}\right)$ . If the block is horizontally displaced through ' $X$ ' $\text{m}$ then the number of complete oscillations it will make in $14\pi$ seconds will be _____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 20

Both springs push back on the block: $k_{eff} = 2K = 4$ N/m.
$T = 2\pi\sqrt{\frac{0.49}{4}} = 2\pi(0.35) = 0.7\pi$ s
Number of oscillations $= \frac{14\pi}{0.7\pi} = 20$

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