JEE Main202528 Jan 2025Evening ShiftPhysicsOscillationsActual
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 . Reason (R): The amplitude and phase can be expressed in terms of x₀ and p ₀ . In the light of the above statements, choos
Options
- A(A) is false but (R) is true
- B(A) is true but (R) is false
- CBoth (A) and (R) are true but (R) is NOT the correct explanation of (A)
- DBoth ( A ) and ( R ) are true and ( R ) is the correct explanation of ( A )
Correct answer
D. Both ( A ) and ( R ) are true and ( R ) is the correct explanation of ( A )
Step-by-step solution
aligned & If we express position x(t)=A ( t+ ) & then x₀=A & v₀=A & = x₀ v₀ & A= x₀^2+ v₀^2 ^2 aligned Hence both position and linear momentum of a particle can be expressed as a function of time if we know initial momentum and position