Position of a Particle in SHM, Displacement and Phase PYQs: JEE Mains Physics

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1. 1. A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm . If D and d are the total distance and displacement covered by the particle in 12.5 s , then \(\frac{\mathrm{D}}{\mathrm{d}}\) is ________. 2025 Easy
2. 2. A simple harmonic oscillator has an amplitude \(A\) and time period \(6 \pi\) second. Assuming the oscillation starts from its mean position, the time required by it to travel from \(x=A\) to \(x=\frac{\sqrt{3}}{2} A\) will be \(\frac{\pi}{x}\) s, where \(x=\) _______. 2024 Hard
3. 3. A particle executes \(S.H.M.\) of amplitude A along \(x\)-axis. At \(t =0\), the position of the particle is \(x=\frac{A}{2}\) and it moves along positive \(x\)-axis the displacement of particle in time \(t\) is \(x=A \sin (\omega t+\delta)\), then the value \(\delta\) will be 2023 Medium
4. 4. A particle executes simple harmonic motion between \(x =- A\) and \(x =+ A\). If time taken by particle to go from \(x=0\) to \(\frac{A}{2}\) is \(2 s\); then time taken by particle in going from \(x =\frac{ A }{2}\) to \(A\) is \(.........\,s\) 2023 Medium
5. 5. A particle executes simple harmonic motion. Its amplitude is \(8 \,cm\) and time period is \(6 \,s\). The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ............. \(s\) 2022 Medium
6. 6. The displacement of simple harmonic oscillator after \(3\) seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is \(\dots \; s\) 2022 Medium
7. 7. Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the \(\sqrt{3}\) times of amplitude of individual motions. The phase difference between the two motions is \(.....(degree)\) 2022 Medium
8. 8. A particle performs simple harmonic motion with a period of \(2\) second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is \(\frac{1}{ a } s .\) The value of \('a'\) to the nearest integer is......... 2021 Medium
9. 9. The point \(A\) moves with a uniform speed along the circumference of a circle of radius \(0.36\, m\) and covers \(30^{\circ}\) in \(0.1\, s\). The perpendicular projection \('P'\) from \('A'\) on the diameter \(MN\) represents the simple harmonic motion of \('P'.\) The restoration force per unit mass when \(P\) touches \(M\) will be ...... \(N\)
   2021 Hard
10. 10. Time period of a simple pendulum is \(T\). The time taken to complete \(5 / 8\) oscillations starting from mean position is \(\frac{\alpha}{\beta} T\). The value of \(\alpha\) is ..... . 2021 Hard
11. 11. \(Y = A \sin \left(\omega t +\phi_{0}\right)\) is the time-displacement equation of a SHM. At \(t=0\) the displacement of the particle is \(Y =\frac{ A }{2}\) and it is moving along negative \(x\) -direction. Then the initial phase angle \(\phi_{0}\) will be ...... . 2021 Hard
12. 12. A simple harmonic oscillator of angular frequency \(2\,rad\,s^{-1}\) is acted upon by an external force \(F = sin\,t\,N .\) If the oscillator is at rest in its equilibrium position at \(t = 0,\) its position at later times is proportional to 2015 Hard

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