First slide

Simple hormonic motion

Question

Infinite springs with force constants k,2 k, 4ft and I k,... respectively are connected in series. The effective force constant of the spring will be

Difficult

A

2k
B

k
C

k /2
D

15 k

Solution

When the springs are connected in series, then
$\frac{1}{k^{'}} = \frac{1}{k} + \frac{1}{2 k} + \frac{1}{4 k} + \frac{1}{8 k} + \dots = \frac{1}{k} [1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots] = \frac{1}{k} [\frac{1}{1 - (1 / 2)}] = \frac{2}{k} k^{'} = k / 2$

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