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BITSAT 2020
Exam
BITSAT
Year
2020
Subject
Physics
Chapter
Oscillations

BITSAT 2020 · Physics · Oscillations

Frequency of oscillation is proportional to

Frequency of oscillation is proportional to Frequency of oscillation is proportional to

Options

  1. A3km\sqrt{\frac{3 \mathrm{k}}{\mathrm{m}}}
  2. Bkm\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}
  3. C2km\sqrt{\frac{2 \mathrm{k}}{\mathrm{m}}}
  4. Dm3k\sqrt{\frac{\mathrm{m}}{3 \mathrm{k}}}

Correct answer

A. 3km\sqrt{\frac{3 \mathrm{k}}{\mathrm{m}}}

Step-by-step solution

Frequency of oscillation is proportional to
Let mass is displaced towards left by xx then force on mass⁡=−kx−2kx=−3kx\operatorname{mass}=-\mathrm{kx}-2 \mathrm{kx}=-3 \mathrm{kx} [negative sign is taken because force is opposite to the direction of motion] ⇒F=−3kx=−mω2x⇒ω=3kmf=ω2π=12π3km\begin{array}{l} \Rightarrow \mathrm{F}=-3 \mathrm{kx}=-\mathrm{m} \omega^{2} \mathrm{x} \Rightarrow \omega=\sqrt{\frac{3 \mathrm{k}}{\mathrm{m}}} \\ \mathrm{f}=\frac{\omega}{2 \pi}=\frac{1}{2 \pi} \sqrt{\frac{3 \mathrm{k}}{\mathrm{m}}} \end{array}Thus it is propotional to \sqrt{3 \mathrm{k} / \mathrm{m}}$
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