Question

Infinite springs with force constant $k,2k,4k,8k$ -------- respectively are connected in series. The effective force constant of the spring will be:

• A. $k/2$
• B. $k$
• C. $2k$
• D. $2048k$

Answer 1

The correct option is A $k/2$

The equivalent spring constant can be given by
$\frac{1}{k_{eq}}=\frac{1}{k}+\frac{1}{2k}+\frac{1}{4k}+\frac{1}{8k}...$
Now, this is a geometric progression, whose sum till infinity can be found out by
$S_{\infty }=\frac{a}{1-r}=\frac{\frac{1}{k}}{1-\frac{1}{2}}=\frac{2}{k}$
$\therefore \frac{1}{k_{eq}}=\frac{2}{k}$
Hence, answer is k/2 and option A is correct.