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Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Knowing initial position x₀ and initial momentum p₀ is enough to determine the position and momentum at any time t for a simple harmonic motion with a given angular frequency ω.
Reason (R): The amplitude and phase can be expressed in terms of x₀ and p₀.
In the light of the above statements, choose the correct answer from the options given below.

Asked in JEE Main 28th Jan 2nd Shift 2025 · Displacement equation and phase

• (1) Both (A) and (R) are true but (R) is not the correct explanation of (A).
• (2) Both (A) and (R) are true and (R) is the correct explanation of (A).
• (3) (A) is false but (R) is true.
• (4) (A) is true but (R) is false.

Step-by-step solution

Why the other options are wrong

• (1) Both statements are true, but this option denies the link. Fixing the amplitude and the phase is exactly what fixes the motion, so (R) is the reason.
• (3) Treats (A) as false. The equation of motion is second order, so two initial conditions are precisely what it needs.
• (4) Treats (R) as false, although A and φ follow directly from x₀ and p₀ by squaring and dividing.

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