A particle of mass 0.1 kg is executing simple harmonic motion of amplitude 0.1 m. When the particle passes through the mean position, its kinetic energy is 8×10-3 J. If the initial phase is 45°, the equation of its motion is (Assume, x t as the position of the particle at time t)

TS EAMCET · Physics · Gravitation

A particle of mass $0.1 kg$ is executing simple harmonic motion of amplitude $0.1 m$ . When the particle passes through the mean position, its kinetic energy is $8 \times 10^{- 3} J$ . If the initial phase is $45 °,$ the equation of its motion is (Assume, $x (t)$ as the position of the particle at time $t$ )

A $x (t) = 0.1 \sin (4 t + \frac{π}{4})$
B $x (t) = 0.1 \sin (16 t + \frac{π}{4})$
C $x (t) = 0.1 \sin (2 (t + \frac{π}{4}))$
D $x (t) = 0.1 \sin (2 t + \frac{π}{4})$

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Answer & Solution

Correct Answer

(A) $x (t) = 0.1 \sin (4 t + \frac{π}{4})$

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Detailed explanation

The mass of particle is m=0.1 kg Amplitude of particle performing SHM is A=0.1 m The initial phase of particle is , ϕ=450=π4 The equation of particle performing SHM is given by x=A sin ωt+ϕ ...1 When the…

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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