As per given figures, two springs of spring constants k and 2k are connected to mass m. If the period of oscillation in figure (a) is 3 s, then the period of oscillation in figure (b) will be √(x) s. The value of x is ___________. Numerical answer type. Work it out, then open the answer.

Answer: 2. (a) series: ka = (k·2k)/(3k) = 2k/3. (b) parallel: kb = 3k. (Tb)/(Ta) = √((ka)/(kb)) = √(2/9) = √(2)/3 Tb = 3×√(2)/3 = √(2) s, so x = 2

As per given figures, two springs of spring constants k and 2k are… | JEE Main 2022 (26 Jul, Shift 2)

Q58JEE Main 2022 · 26 JUL · SHIFT 2Medium

Spring Systems

As per given figures, two springs of spring constants $k$ and $2k$ are connected to mass $m$ . If the period of oscillation in figure (a) is $3\text{ s}$ , then the period of oscillation in figure (b) will be $\sqrt{x}\text{ s}$ . The value of $x$ is ___________.

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

Show answer and solution

Answer: 2

(a) series: $k_a = \frac{k\cdot2k}{3k} = \frac{2k}{3}$ . (b) parallel: $k_b = 3k$ .
$\frac{T_b}{T_a} = \sqrt{\frac{k_a}{k_b}} = \sqrt{\frac{2}{9}} = \frac{\sqrt{2}}{3}$
$T_b = 3\times\frac{\sqrt{2}}{3} = \sqrt{2}$ s, so $x = 2$

Report a mistake

Spring Systems question from JEE Main 2022 (26 Jul, Shift 2)

More questions on Spring Systems