Question 207: Oscillations

Question

As shown in the figure, $S_1$ and $S_2$ are identical springs with spring constant K each. The oscillation frequency of the mass ' $m$ ' is ' $f$ '. If the spring $\mathrm{S}_2$ is removed, the oscillation frequency will become

Accepted Answer

Case 1: With both springs $S_1 \& S_2$
Effective spring constant: $K_{	ext {eff }}: K+K=2 K$
Oscillation frequency: $f=\frac{1}{2 \pi} \sqrt{\frac{K_{	ext {eff }}}{m}}=\frac{1}{2 \pi} \sqrt{\frac{2 K}{m}}$
Case II: After removing $S_2$
Now only one spring with spring constant K
New frequency: $\mathrm{f}^{\prime}=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{~K}}{\mathrm{~m}}}$
Divide both cases: $\frac{F^{\prime}}{F}=\frac{\sqrt{\frac{K}{m}}}{\sqrt{\frac{2 K}{m}}}$
$$ \begin{array}{ll} \Rightarrow & \frac{F^{\prime}}{F}=\frac{1}{\sqrt{2}} \ 	herefore & F^{\prime}=\frac{F}{\sqrt{2}} \end{array} $$

Answer

f

Answer

2 f

Answer

$\frac{\mathrm{f}}{\sqrt{2}}$

Answer

$\sqrt{2} \cdot \mathrm{f}$

Oscillations

As shown in the figure, S_1 and S_2 are identical springs with spring constant K each. The oscillation frequency of the mass ' m ' is ' f '. If the spring \mathrm{S}_2 is removed, the oscillation frequency will become

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