AP EAMCET · PHYSICS · Oscillations

The displacements of two particles of same mass executing SHM are represented by the equations
\(x_1=4 \sin \left(10 t+\frac{\pi}{6}\right) \text { and } x_2=5 \cos (\omega t) .\)
The value of \(\omega\) for which the energies of both the particles remain same is

A 16 unit
B 6 unit
C 4 unit
D 8 unit

Verified Solution

Answer & Solution

Correct Answer

(D) 8 unit

Step-by-step Solution

Detailed explanation

The equation of displacement \(x_1=4 \sin \left(10 t+\frac{\pi}{6}\right)\) The energy of this equation \(E_1=\frac{1}{2} m \omega_1^2 a_1^2\) \(=\frac{1}{2} m \times 10 \times 10 \times 4 \times 4\) The second equation of displacement \(x_2=5 \cos (\omega t)\) The energy of…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The displacements of two particles of same mass executing SHM are represented by the equations\(x_1=4 \sin \left(10 t+\frac{\pi}{6}\right) \text { and } x_2=5 \cos (\omega t) .\)The value of \(\omega\) for which the energies of both the particles remain same is

Step-by-step Solution

The displacements of two particles of same mass executing SHM are represented by the equations
\(x_1=4 \sin \left(10 t+\frac{\pi}{6}\right) \text { and } x_2=5 \cos (\omega t) .\)
The value of \(\omega\) for which the energies of both the particles remain same is