Second's Pendulum Find its Length and Frequency

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Learn about the Second's Pendulum in Class 11 Physics Chapter 13 Oscillation with its definition, formula, derivation, length, frequency, numerical. Easy NCERT-based notes JEE NEET - Physics kund 

Second's Pendulum

A second's pendulum is a simple pendulum whose time period (T) is 2 seconds.

Formula for Time Period

\[ T = 2\pi \sqrt{\frac{L}{g}} \]

Squaring both sides,

\[ T^2 = \frac{4\pi^2L}{g} \]

Therefore, the length of the pendulum is

\[ L = \frac{T^2g}{4\pi^2} \]

Calculation of Length

For a second's pendulum,

  • \(T = 2\;s\)
  • \(g = 9.8\;m/s^2\)

\[ L = \frac{(2)^2 \times 9.8}{4\pi^2} = \frac{39.2}{39.48} \approx 0.993\;m \approx 1\;m \]

Hence, the length of a second's pendulum is \[ L \approx 1\;m = 100\;cm \]

Frequency of Second's Pendulum

Frequency is given by

\[ f=\frac{1}{T} \]

\[ f=\frac{1}{2}=0.5\;Hz \]

Final Result

  • Time Period: \(2\;s\)
  • Length: \(0.993\;m \approx 1\;m = 100\;cm\)
  • Frequency: \(0.5\;Hz\)

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