Physics Waves SZABMU 2023
PMDC Verified Question 36 of 125
Time period of a vibrating body is independent of:
A
Frequency
B
Amplitude
C
Wavelength
D
Value of 'g'
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: Amplitude
Concept:

In Simple Harmonic Motion (like a simple pendulum or an ideal spring), the oscillation timing is defined by system constants.

Formula:

$$ T = 2\pi\sqrt{\frac{L}{g}} \quad \text{or} \quad T = 2\pi\sqrt{\frac{m}{k}} $$

Solution:

  • Notice that neither formula contains the variable for amplitude (maximum displacement).


  • This remarkable property is called isochronism: whether the body swings slightly or a bit more widely, it takes the exact same amount of time to complete one full cycle.


  • Therefore, the time period is independent of Amplitude.


Why other options are incorrect:

Time period is the exact mathematical inverse of frequency (\( T = 1/f \)), making it entirely dependent on it. It also clearly depends on 'g' for pendulums.

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