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:

  1. (d) The effective spring constant of two springs in series; $K=\frac{k_1 k_2}{k_1+k_2}$.

Time period,

$T=2 \pi \sqrt{\frac{m}{K}}=2 \pi \sqrt{\frac{m(k_1+k_2)}{k_1 k_2}}$