MHT CET · Physics · Oscillations

A particle performing S.H.M. starts from the equilibrium position and its time period is $16$ seconds. After $2$ seconds its velocity is $π m s^{- 1} .$ Amplitude of oscillation is $(\cos 45^{o} = \frac{1}{\sqrt 2})$

A $2 \sqrt{2} m$
B $4 \sqrt{2} m$
C $6 \sqrt{2} m$
D $8 \sqrt{2} m$

Verified Solution

Answer & Solution

Correct Answer

(D) $8 \sqrt{2} m$

Step-by-step Solution

Detailed explanation

Displacement of the particle

= x = A \sin ω t

The velocity of the particle

= v = \frac{d x}{d t} = A ω \cos ω t

v = π m s^{- 1}, T = 16 s, ω = \frac{2 π}{T} = \frac{2 π}{16} = \frac{π}{8} rad s^{- 1}

∴ π = A \times \frac{π}{8} \times \cos \frac{π}{8} \times 2

∴ 1 = \frac{A}{8} \cos \frac{π}{4} = \frac{A}{8} . \frac{1}{\sqrt 2}

∴ A = 8 \sqrt{2} m

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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A particle performing S.H.M. starts from the equilibrium position and its time period is 16 seconds. After 2 seconds its velocity is π m s-1. Amplitude of oscillation is cos⁡45o=1√2

Step-by-step Solution

A particle performing S.H.M. starts from the equilibrium position and its time period is $16$ seconds. After $2$ seconds its velocity is $π m s^{- 1} .$ Amplitude of oscillation is $(\cos 45^{o} = \frac{1}{\sqrt 2})$