How Does Phase Affect Direction in Simple Harmonic Motion?

[thunderhadron]

Hi friends the problem is -

https://fbcdn-sphotos-e-a.akamaihd.net/hphotos-ak-ash4/430884_2656507629229_1511525381_n.jpg

Attempt -
friend as per the question I am trying to get structure of SHM,

The displacement equation x = A sin(ωt + θ) represents SHM where ωt + θ is Phase of the particle.

the phase of the particle is 13∏/6. So I putting it on the equation and getting the result -

x = A/2. So I am getting the first answer.

While differentiating the displacement equation w.r.t. time I'll get velocity - time equation.

Which will be,

v = A.ω cos(ωt + θ)

Placing here the Phase of the particle I am getting the result,

v = A.ω.√3 / 2

So i am sticking here, is it representing the direction of the particle too ?

The correct answer of this problem is option (A) as per the question.

Please friends help me in solving this Problem.

Thank you all in advance.

 

[TSny]

v = A.ω.√3 / 2

is it representing the direction of the particle too ?

Yes, the direction the particle is moving is the direction of the velocity. You got a positive velocity which indicates the velocity has a direction toward positive X.

Check that if the phase were 17π/6, then the particle would be moving in -X direction.

 

[thunderhadron]

Yes, the direction the particle is moving is the direction of the velocity. You got a positive velocity which indicates the velocity has a direction toward positive X.

Check that if the phase were 17π/6, then the particle would be moving in -X direction.

Thank you TSny.

I got the correct answer and concept