Energy of Simple Harmonic Motion PYQs: JEE Mains Physics

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1. 1. The displacement of a particle, executing simple harmonic motion with time period \(T\), is expressed as \(x(t)= A \sin \omega t\), where \(A\) is the amplitude. The maximum value of potential energy of this oscillator is found at \(t=T / 2 \beta\). The value of \(\beta\) is ___________. 2026 Medium
2. 2. The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of \(176 rad / s\). The frequency of this simple harmonic oscillator is _________ Hz. \(\left[\right.\) take \(\left.\pi=\frac{22}{7}\right]\) 2026 Medium
3. 3. An object of mass \(0.2 \mathrm{~kg}\) executes simple harmonic motion along \(\mathrm{x}\) axis with frequency of \(\left(\frac{25}{\pi}\right) \mathrm{Hz}\). At the position \(\mathrm{x}=0.04 \mathrm{~m}\) the object has kinetic energy \(0.5 \mathrm{~J}\) and potential energy \(0.4 \mathrm{~J}\) The amplitude of oscillation is _______ cm. 2024 Hard
4. 4. In simple harmonic motion, the total mechanical energy of given system is E. If mass of oscillating particle \(P\) is doubled then the new energy of the system for same amplitude is _______.
   2024 Hard
5. 5. When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is \(\frac{x}{8}\), where \(x=\) _______. 2024 Hard
6. 6. A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is on 2023 Medium
7. 7. A particle is executing Simple Harmonic Motion \((SHM)\). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be 2023 Medium
8. 8. At a given point of time the value of displacement of a simple harmonic oscillator is given as \(y = A \cos \left(30^{\circ}\right)\). If amplitude is \(40\,cm\) and kinetic energy at that time is \(200\, J\), the value of force constant is \(1.0 \times 10^{ x }\,Nm ^{-1}\). The value of \(x\) is ...... 2023 Hard
9. 9. The amplitude of a particle executing \(SHM\) is \(3\,cm\). The displacement at which its kinetic energy will be \(25 \%\) more than the potential energy is: \(.............cm\). 2023 Medium
10. 10. The general displacement of a simple harmonic oscillator is \(x = A \sin \omega t\). Let \(T\) be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when \(t=\frac{T}{\beta}\). The value of \(\beta\) is \(.........\) 2023 Hard
11. 11. The maximum potential energy of a block executing simple harmonic motion is \(25\,J\). A is amplitude of oscillation. At \(A / 2\), the kinetic energy of the block is \(...............\) 2023 Easy
12. 12. A body is performing simple harmonic with an amplitude of \(10 \,cm\). The velocity of the body was tripled by air Jet when it is at \(5 \,cm\) from its mean position. The new amplitude of vibration is \(\sqrt{ x } \,cm\). The value of \(x\) is________ 2022 Hard
13. 13. A mass \(0.9\,kg\), attached to a horizontal spring, executes \(SHM\) with an amplitude \(A _{1}\). When this mass passes through its mean position, then a smaller mass of \(124\,g\) is placed over it and both masses move together with amplitude \(A _{2}\). If the ratio \(\frac{ A _{1}}{ A _{2}}\) is \(\frac{\alpha}{\alpha-1}\), then the value of \(\alpha\) will be\(......\) 2022 Hard
14. 14. The potential energy of a particle of mass \(4\,kg\) in motion along the \(x\)-axis is given by \(U =4(1-\cos 4 x )\,J\). The time period of the particle for small oscillation \((\sin \theta \simeq \theta)\) is \(\left(\frac{\pi}{ K }\right)\,s\). The value of \(K\) is ....... 2022 Hard
15. 15. A particle of mass \(1\, {kg}\) is hanging from a spring of force constant \(100\, {Nm}^{-1 .}\) The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period \({T}\). The time when the kinetic energy and potential energy of the system will become equal, is \(\frac{{T}}{{x}}\). The value of \({x}\) is ..... . 2021 Hard
16. 16. A particle starts simple harmonic motion from the mean position. Its amplitude is \(a\) and total energy \(E\). At one instant its kinetic energy is \(3E/4.\) Its displacement at that instant is 2021 Medium
17. 17. An object of mass \(0.5\, {kg}\) is executing simple harmonic motion. Its amplitude is \(5\, {cm}\) and time period (T) is \(0.2\, {s} .\) What will be the potential energy of the object at an instant \(t=\frac{T}{4}\) s starting from mean position. Assume that the initial phase of the oscillation is zero. (In \({J}\)) 2021 Medium
18. 18. For a body executing \(S.H.M. :\) \((a)\) Potential energy is always equal to its \(K.E.\) \((b)\) Average potential and kinetic energy over any given time interval are always equal. \((c)\) Sum of the kinetic and potential energy at any point of time is constant. \((d)\) Average \(K.E.\) in one time period is equal to average potential energy in one time period. Choose the most appropriate option from the options given below: 2021 Medium
19. 19. In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position. 2021 Medium
20. 20. The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal, when displacement (amplitude = \(a\)) is 2021 Medium
21. 21. The displacement time graph of a particle executing \(S.H.M.\) is given in figure: (sketch is schematic and not to scale) Which of the following statements is are true for this motion? \((A)\) The force is zero \(t=\frac{3 T}{4}\) \((B)\) The acceleration is maximum at \(t=T\) \((C)\) The speed is maximum at \(t =\frac{ T }{4}\) \((D)\) The \(P.E.\) is equal to \(K.E.\) of the oscillation at \(t=\frac{T}{2}\)
    2020 Hard
22. 22. A massless spring \((k = 800\, N/m)\), attached with a mass \((500\, g)\) is completely immersed in \(1\, kg\) of water. The spring is stretched by \(2\, cm\) and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass \(= 400\, J/kg\, K\), specific heat of water \(= 4184\, J/kg\, K\)) 2019 Hard
23. 23. A particle is executing simple harmonic motion \((SHM)\) of amplitude \(A,\) along the \(x-\) axis, about \(x = 0.\) When its potential energy \((PE)\) equals kinetic energy \((KE),\) the position of the particle will be 2019 Medium
24. 24. A particle undergoing simple harmonic motion has time dependent displacement given by \(x(t)\, = \,A\,\sin \,\frac{{\pi t}}{{90}}\). The ratio of kinetic to potential energy \(o\) the particle at \(t=210\,s\) will be 2019 Medium
25. 25. A pendulum is executing simple harmonic motion and its maximum kinetic energy is \(K_1\). If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is \(K_2\) then 2019 Medium
26. 26. An oscillator of mass \(M\)  is at rest in its equilibrium position in a potential \(V\, = \,\frac{1}{2}\,k{(x - X)^2}.\) A particle of mass \(m\)  comes from right with speed \(u\)  and collides completely inelastically with \(M\) and sticks to it . This process repeats every time the oscillator crosses its equilibrium position .The amplitude of oscillations after \(13\)  collisions is: \((M = 10,\, m = 5,\, u = 1,\, k = 1 ).\)  2018 Hard
27. 27. A block of mass \(0.1\, kg\) is connected to an elastic spring of spring constant \(640\, Nm^{-1}\) and oscillates in a damping medium of damping constant \(10^{-2}\, kg\,s^{-1}\) . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to ..... \(s\) 2017 Hard
28. 28. A pendulum with time period of \(1\, s\) is losing energy due to damping. At certain time its energy is \(45\, J\). If after  completing \(15\,oscillations\) , its energy has become \(15\, J\), its damping constant (in \(s^{-1}\) ) is 2015 Medium
29. 29. Two springs of force constants \(300\, N/m\) (Spring \(A\)) and \(400\, N/m\) (Spring \(B\)) are joined together in series . The combination is compressed by \(8.75\, cm\). The ratio of energy stored in \(A\) and \(B\) is  \(\frac{{{E_A}}}{{{E_B}}}\).  Then \(\frac{{{E_A}}}{{{E_B}}}\) is equal to 2013 Hard

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