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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 ω t (2) x = A sin ω t (3) x = -A + A cos ω t (4) x = A – Acos ω t

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

Grade:12

1 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
Dear student,

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

But if the center is shifted by A, the equation becomesx=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}
Hencex=A-Acos\omega t

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