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Superposition of Two SHMs for JEE: 13 solved questions

Real JEE paper questions on superposition of two shms, part of oscillations. Each opens with the options, the correct answer and a step-by-step solution. Papers run from 2003 to 2025. No sign-in needed to read them.

What this topic asks

• Resultant amplitude and phase — 11 questions
• Lissajous figures — 2 questions

All 13 questions with solutions

• A particle is subjected to two simple harmonic motions x₁=√7 sin 5t cm and x₂=2√7 sin (5t+π/3) cm, with t in… JEE Main 2nd April 1st Shift 2025
• For a periodic motion represented by y=sin ω t+cos ω t, the amplitude of the motion is JEE Main 10th April 2nd Shift 2023
• The equations of two waves on a string are y₁=5 sin 2π(x-vt) cm and y₂=3 sin 2π(x-vt+1.5) cm, and they pass t… JEE Main 24th June 1st Shift 2022
• A simple harmonic motion is represented by y=5(sin 3π t+√3 cos 3π t) cm. The amplitude and time period of the… JEE Main 12th Jan 2nd Shift 2019
• Two simple harmonic motions at right angles, x(t)=A sin(at+δ) and y(t)=B sin(bt), are combined to form Lissaj… JEE Main Online 2018
• The x and y displacements of a particle are x(t)=a sin ω t and y(t)=a sin 2ω t. Its trajectory will look like JEE Main Online 2015
• Two particles execute simple harmonic motion of the same amplitude A and frequency ω along the x-axis. Their… JEE Main 2011
• Two simple harmonic motions are represented by y₁=0.1 sin (100π t+π/3) and y₂=0.1 cos π t. The phase differen… JEE Main 2005
• The displacement of a particle varies as x=4(cos π t+sin π t). The amplitude of the particle is JEE Main 2003
• Two simple harmonic waves of equal amplitude 8 cm and equal frequency 10 Hz travel in the same direction. The… JEE Main 29th Jan 1st Shift 2023
• Two waves travelling in the same direction with the same amplitude and frequency are superposed. The resultan… JEE Main 25th July 2nd Shift 2022
• Two simple harmonic motions are x₁=5 sin (2π t+π/4) and x₂=5√2(sin 2π t+cos 2π t). The amplitude of the secon… JEE Main 26th Aug 2nd Shift 2021
• Two simple harmonic motions are y₁=10 sin (3π t+π/3) and y₂=5(sin 3π t+√3 cos 3π t). The ratio of the amplitu… JEE Main 27th Aug 2nd Shift 2021