Velocity of Simple Harmonic Motion PYQs: JEE Mains Physics

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1. 1. The equation of motion of a particle is given by \(x = a \sin\left(50t + \dfrac{\pi}{3}\right)\) cm. The particle will come to rest at time \(t_1\) and it will have zero acceleration at time \(t_2\). The \(t_1\) and \(t_2\) respectively are _______. 2026 Medium
2. 2. The velocity of a particle executing simple harmonic motion along \(x\)-axis is described as \(v^2 = 50 - x^2\), where \(x\) represents displacement. If the time period of motion is \(\dfrac{x}{7}\) s, the value of \(x\) is _____. 2026 Medium
3. 3. Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
   Assertion (A) : Knowing initial position \(x_0\) and initial momentum \(p_0\) is enough to determine the position and momentum at any time \(t\) for a simple harmonic motion with a given angular frequency \(\omega\).
   Reason (R): The amplitude and phase can be expressed in terms of \(x_0\) and \(\mathrm{p}_0\).
   In the light of the above statements, choose the correct answer from the options given below : 2025 Easy
4. 4. Two bodies A and B of equal mass are suspended from two massless springs of spring constant \(k_1\) and \(k_2\), respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of \(A\) to the maximum velocity of \(B\) is _______. 2025 Easy
5. 5. A particle executes simple harmonic motion with an amplitude of \(4 \mathrm{~cm}\). At the mean position, velocity of the particle is \(10 \mathrm{~cm} / \mathrm{s}\). The distance of the particle from the mean position when its speed becomes \(5 \mathrm{~cm} / \mathrm{s}\) is \(\sqrt{\alpha} \mathrm{cm}\), where \(\alpha=\)____________. 2024 Hard
6. 6. A particle is doing simple harmonic motion of amplitude \(0.06 \mathrm{~m}\) and time period \(3.14 \mathrm{~s}\). The maximum velocity of the particle is _______ \(\mathrm{cm} / \mathrm{s}\). 2024 Hard
7. 7. A particle performs simple harmonic motion with amplitude \(A\). Its speed is trebled at the instant that it is at a distance \(\frac{{2A}}{3}\) from equilibrium position. The new amplitude of the motion is 2024 Hard
8. 8. A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is \(\frac{2 \mathrm{~A}}{3}\). The new amplitude of motion is \(\frac{\mathrm{nA}}{3}\). The value of \(\mathrm{n}\) is____. 2024 Hard
9. 9. The displacement of a particle executing SHM is given by \(x=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{m}\). The time period of motion is \(3.14 \mathrm{~s}\). The velocity of the particle at \(\mathrm{t}=0\) is_________ \(\mathrm{m} / \mathrm{s}\). 2024 Hard
10. 10. The velocity of a particle executing SHM varies with displacement \(( x )\) as \(4 v ^2=50- x ^2\). The time period of oscillations is \(\frac{x}{7} s\). The value of \(x\) is \(............\) \(\left(\right.\) Take \(\left.\pi=\frac{22}{7}\right)\) 2023 Medium
11. 11. The equation of a particle executing simple harmonic motion is given by \(x =\sin \pi\left( t +\frac{1}{3}\right) m\). At \(t =1 \,s\), the speed of particle will be .......... \(cm s ^{-1}\) (Given : \(\pi=3.14\) ) 2022 Medium
12. 12. Two massless springs with spring constants \(2\,k\) and \(9\,k\), carry \(50\, g\) and \(100 \,g\) masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be 2022 Easy
13. 13. When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be. 2022 Medium
14. 14. A particle executes \(S.H.M.,\) the graph of velocity as a function of displacement is :- 2021 Medium
15. 15. A particle executes \(S.H.M.\) with amplitude \('a'\) and time period \(V\). The displacement of the particle when its speed is half of maximum speed is \(\frac{\sqrt{ x } a }{2} .\) The value of \(x\) is \(\ldots \ldots \ldots\) 2021 Medium
16. 16. A particle executes simple harmonic motion represented by displacement function as \(x(t)=A \sin (\omega t+\phi)\) If the position and velocity of the particle at \(t=0\, {s}\) are \(2\, {cm}\) and \(2\, \omega \,{cm} \,{s}^{-1}\) respectively, then its amplitude is \(x \sqrt{2} \,{cm}\) where the value of \(x\) is ..... . 2021 Medium
17. 17. When a particle executes \(SHM\) the nature of graphical representation of velocity as a function of displacement is : 2021 Medium
18. 18. The position co-ordinates of a particle moving in a \(3-D\) coordinates system is given by \(x = a\,cos\,\omega t\) , \(y = a\,sin\,\omega t\) and \(z = a\omega t\) The speed of the  particle is 2019 Medium
19. 19. A body is in simple harmonic motion with time period half second \((T\, = 0.5\, s)\) and amplitude one \(cm\, (A\,= 1\, cm)\). Find the average velocity in the interval in which it moves form equilibrium position to half of its amplitude .... \(cm/s\) 2014 Medium

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