JEE Main20238 Apr 2023Evening ShiftPhysicsOscillationsActual
For particle P revolving round the centre O with radius of circular path r and regular velocity ω , as shown in below figure, the projection of O P on the x -axis at time t is
Options
- Ax ( t ) = r   cos ω t - π 6
- Bx ( t ) = r   cos ω t + π 6
- Cx ( t ) = r   sin ω t + π 6
- Dx ( t ) = r   cos ( ω t )
Correct answer
B. x ( t ) = r   cos ω t + π 6
Step-by-step solution
As can be seen from the diagram, the initial phase of the particle is given by φ = 30 ° =   π 6 The equation of motion of the particle at its initial position at time t = 0 can be written as x t = r cos θ       . . . ( 1 ) where, θ is the angular displacement of the particle at time t = t . Since, the position of the particle at a later instant of time always lags behind its initial position at time t = 0 , the equation of motion of the particle at any instant of time is