Physics Waves ETEA 2014
PMDC Verified Question 115 of 125
The displacement '\( x \)' of a particle at time '\( t \)' is given by \( x= 10 \sin 4t \) the particle oscillates with period.
A
\( \pi/10\text{s} \)
B
\( \pi/5\text{s} \)
C
\( \pi/4\text{s} \)
D
\( \pi/2\text{s} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \( \pi/2\text{s} \)
Concept:

The general equation for a particle executing Simple Harmonic Motion is given by \( x = x_0 \sin(\omega t) \).

Formula:

$$ \omega = \frac{2\pi}{T} $$

Solution:

  • By comparing the given equation \( x = 10 \sin(4t) \) to the standard form, we can extract the angular frequency: \( \omega = 4 \text{ rad/s} \).


  • Rearrange the period formula: \( T = \frac{2\pi}{\omega} \).


  • Substitute \( \omega \): \( T = \frac{2\pi}{4} = \frac{\pi}{2} \text{ s} \).


Why other options are incorrect:

Students might mistakenly divide the amplitude (10) by 4 or incorrectly invert the period formula.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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