Question

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 3s, then the period of oscillation in figure (b) will be $\sqrt x$ s. The value of $x$ is _______

Answer 1

For case (a),

$k_{eq}=\frac{2K}{3}$

For case (b),

$k_{eq}=3k$

$∵T=2π\sqrt{\frac{m}{k}}$

$∴ \frac{T_a}{T_b}=\sqrt{\frac{K_b}{K_a}}$

$\frac{3}{T_b}=\sqrt{\frac{3K×3}{2k}}=\frac{3}{\sqrt{2}}$

$T_b = \sqrt2$

$x = 2$