Oscillations Ques 63
63. A mass $m$ is suspended from a two coupled springs, connected in series. The force constant for springs are $k_1$ and $k_2$. The time period of the suspended mass will be
[1990]
(a) $T=2 \pi \sqrt{\frac{m}{k_1-k_2}}$
(b) $T=2 \pi \sqrt{\frac{m k_1 k_2}{k_1+k_2}}$
(c) $T=2 \pi \sqrt{\frac{m}{k_1+k_2}}$
(d) $T=2 \pi \sqrt{\frac{m(k_1+k_2)}{k_1 k_2}}$
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Answer:
Correct Answer: 63.(d)
Solution:
- (d) The effective spring constant of two springs in series; $K=\frac{k_1 k_2}{k_1+k_2}$.
Time period,
$T=2 \pi \sqrt{\frac{m}{K}}=2 \pi \sqrt{\frac{m(k_1+k_2)}{k_1 k_2}}$
BETA
