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Simple Harmonic Motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsSimple Harmonic Motion5 Marks
Question
A simple pendulum is constructed by hanging a heavy ball by a $5.0m$ long string. It undergoes small oscillations.
  1. How many oscillations does it make per second?
  2. What will be the frequency if the system is taken on the moon where acceleration due to gravitation of the moon is $1.67m/s^2$.
✓

Answer

$\text{L}=5\text{m}$
  1. $\text{T}=2\pi\sqrt{\frac{\ell}{\text{g}}}=2\pi\sqrt{0.5}=2\pi(0.7)$
$\therefore$ in $2\pi(0.7)\sec$ the body completes 1 oscillation,
In 1 second, the body will complete $\frac{1}{2\pi(0.7)}$ oscillation
$\therefore\text{f}=\frac{1}{2\pi(0.7)}=\frac{10}{14\pi}=\frac{0.70}{\pi}$ Times
  1. When it is taken to the moon
$\text{T}=2\pi\sqrt{\frac{\ell}{\text{g'}}}$ where g' → Acceleration in the moon.
$=2\pi\sqrt{\frac{5}{1.67}}$
$\therefore\text{f}=\frac{1}{\text{T}}=\frac{1}{2\pi}\sqrt{\frac{1.67}{5}}=\frac{1}{2\pi}(0.577)=\frac{1}{2\pi\sqrt{3}}$ times.

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