Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Knowing initial position x 0 and initial momentum p 0 is enough to determi

Question

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Knowing initial position x 0 ​ and initial momentum p 0 ​ 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 x 0 ​ and p 0 ​ . In the light of the above statements, choose the correct answer from the options given below :

TestHub · Accepted Answer

​ If we express position x ( t ) = A sin ( ω t + ϕ ) then x 0 ​ = A sin ϕ v 0 ​ = A ω cos ϕ ⇒ tan ϕ = v 0 ​ ω x 0 ​ ​ A = x 0 2 ​ + ω 2 v 0 2 ​ ​ ​ ​ Hence both position and linear momentum of a particle can be expressed as a function of time if we know initial momentum and position

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Options:

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