Question

In each of the following questions, Match column I and column II and select the correct match out of the four given choices.

Answer 1

In figure (A), the effective spring constant, $K=$ $k_1+k_2$

In figure (B), the effective spring constant $\frac{1}{K}=\frac{1}{k_1}+\frac{1}{k_2}$ or $K=\frac{k_1{k}_2}{(k_1+k_2)}$

In figure (C), the effective spring constant, $K=k+k=2k$

In figure (D), let the effective spring constant be $K$.

If mass $m$ be pulled down by distnace $y$, the springs A and B will be stretched by $y^{\prime }(=ycos$${45}^{\circ }$ )

Total restoring force is $F=Ky=$ $F_{A}cos{45}^{\circ }+F_{b}cos{45}^{\circ }=2\left(k{y}^{\prime }\right)cos{45}^{\circ }=2k\left(ycos{45}^{\circ }\right)cos{45}^{\circ }$ $=ky$

$\therefore$ $K=k$; and time period $T=$$2\pi \sqrt{\frac{m}{K}}$