First slide

Spring forces

Question

Two identical springs of constant k are connected in series and parallel as shown in figure. A mass M is suspended from them. The ratio of their frequencies of vertical oscillations will be:

Easy

A

2 : 1
B

1 : 2
C

1 : 4
D

4 : 1

Solution

Spring constants are, $\frac{k}{2}$ and 2k
$n α \sqrt{k} \frac{n_{1}}{n_{2}} = \sqrt{\frac{k / 2}{2 k}} = \frac{1}{2}$

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