MHTCET 13 Apr 2026 Shift 1 Paper

Concept:In a stationary wave, the time period of oscillation is the same for all particles, but the amplitude depends on the position of the particle.Explanation:The displacement of a particle in a stationary wave is given by:$$y = 2a \sin kx \cos \omega t$$For a fixed particle at position $x$, the term $2a \sin kx$ acts as the amplitude of that particle.The term $\cos \omega t$ shows that every vibrating particle has the same angular frequency $\omega$.Hence, all particles have the same time period.However, the amplitude $2a \sin kx$ changes with position $x$.At nodes, $\sin kx = 0$, so the amplitude becomes zero and the particles do not vibrate.At all other points, the amplitude is non-zero and different for different positions.Therefore, all particles except nodes vibrate in S.H.M. with the same period but different amplitudes.Answer:Option A: except at nodes vibrate in S.H.M. of same period but of different amplitudes.