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Grade 12General Physics

A particle executes SHM along the x-axis and has the center of oscillation at x = A. The angular frequency of the oscillations is ω and amplitude is A. Initially, the particle is at rest at the origin. Which of the following represents the equation of position of the particle ?

(1) x = –A sin ωt
(2) x = A sin ωt
(3) x = -A + A cos ωt
(4) x = A – Acosωt

Aslan

8 Years agoGrade 12

1 Answer

Eshan

8 Years ago

Dear student,

Equation of SHM with center at origin is $x=A sin(\omega t+\phi_0)$

But if the center is shifted by A, the equation becomes $x=A+A sin(\omega t+\phi_0)$
Now the particle starts from x=0.

Hence at t=0, x=0

$\implies 0=A + Asin\phi_0$
$\implies sin\phi_0\implies \phi_0=\dfrac{3\pi}{2}$
Hence $x=A-Acos\omega t$

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