Q 11-13-072JEE MainJEE Main 2023 (31 Jan, Shift 1)Medium
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 ($K=2\ \text{N m}^{-1}$). If the block is horizontally displaced through $X$ m then the number of complete oscillations it will make in $14\pi$ seconds will be ______.
Numerical value type. Enter your answer.
Answer: 20
Both springs act on the block together: $k_{eff}=2K=4\ \text{N m}^{-1}$.
$$T=2\pi\sqrt{\frac{m}{k_{eff}}}=2\pi\sqrt{\frac{0.49}{4}}=2\pi\times0.35=0.7\pi\ \text{s}$$
Number of oscillations in $14\pi\ \text{s}$ $=\dfrac{14\pi}{0.7\pi}=20$.
Solution by Sreeraj P, M.Sc Physics