Oscillations - Result Question 60
65. 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) $T=2 \pi \sqrt{\frac{m(k_1+k_2)}{k_1 k_2}}$
Topic 4: Damped SHM, Forced Ocillations
& Resonance66. The damping force on an oscillator is directly proportional to the velocity. The unit of the constant of proportionality is:
(a) $kgms^{-1}$
(c) $kgs^{-1}$
(b) $kgms^{-2}$
(d) $kgs$
[2012]
Show Answer
Solution:
- (d) The effective spring constant of two springs in series; $K=\frac{k_1 k_2}{k_1+k_2}$.
Time period,
$T=2 \pi \sqrt{\frac{m}{K}}=2 \pi \sqrt{\frac{m(k_1+k_2)}{k_1 k_2}}$
