STD 11 - Oscillations PYQs: JEE Mains Physics

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1. 1. A cylindrical block of mass M and area of cross section A is floating in a liquid of density \(\rho\) and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is _________ . 2026 Medium
2. 2. A particle is executing simple harmonic motion. Its amplitude is \(A\) and time period is \(5\) sec. The time required by it to move from \(x = A\) to \(x = \dfrac{A}{\sqrt{2}}\) is _______ sec. 2026 Medium
3. 3. A simple pendulum of string length 30 cm performs 20 oscillations in 10s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration is ___________ cm. [Assume that the mass of the pendulum remains same.] 2026 Easy
4. 4. A spring of force constant \(15 N / m\) is cut into two pieces. If the ratio of their length is \(1: 3\), then the force constant of smaller piece is _________ N/m 2026 Easy
5. 5. A spring stretches by \(2\) mm when it is loaded with a mass of \(200\) g. From equilibrium position the mass is further pulled down by \(2\) mm and released. The frequency associated with the system and maximum energy in the spring are __________ Hz and __________ J, respectively. (Take g \(= 10\) m/s\(^2\)) 2026 Hard
6. 6. A uniform disc of radius \(R\) and mass \(M\) is free to oscillate about the axis \(A\) as shown in the figure. For small oscillations the time period is ______.
   (\(g\) is acceleration due to gravity)
   2026 Hard
7. 7. An object of uniform density rolls up the curved path with the initial velocity \(v_0\) as shown in the figure. If the maximum height attained by an object is \(\dfrac{7v_0^2}{10g}\) (\(g\) = acceleration due to gravity), the object is a _______.
   2026 Medium
8. 8. As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of the system is :
   2026 Hard
9. 9. Match List-I with List-II.
   

   List-I	List-II
   A. \(\sin^2 \omega t\)	I. Periodic with time period \(T = \dfrac{\pi}{\omega}\) but not simple harmonic motion (SHM)
   B. \(\sin^3(2\omega t)\)	II. Periodic with time period \(T = \dfrac{2\pi}{\omega}\) but Not SHM
   C. \(\sin(\omega t) + \cos(\pi \omega t)\)	III. Periodic with time period \(T = \dfrac{\pi}{\omega}\) and SHM
   D. \(\cos\omega t + \cos 2\omega t\)	IV. Non-periodic

   
   Choose the correct answer from the options given below : 2026 Hard
10. 10. 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
11. 11. 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
12. 12. The frequency of oscillation of a mass \(m\) suspended by a spring is \(v_1\). If the length of the spring is cut to half, the same mass oscillates with frequency \(v_2\). The value of \(v_2/v_1\) is ________. 2026 Medium
13. 13. 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
14. 14. 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
15. 15. A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is \(y \pi \times 10^{-2} \mathrm{~s}\), where the value of \(y\) is ________.
    (Acceleration due to gravity, \(g=10 \mathrm{~m} / \mathrm{s}^2\), density of water \(=10^3 \mathrm{~kg} / \mathrm{m}^3\) ) 2025 Hard
16. 16. 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
17. 17. A particle is subjected two simple harmonic motions as :
    \(\mathrm{x}_1=\sqrt{7} \sin 5 \mathrm{tcm}\)
    and \(x_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}\right) \mathrm{cm}\)
    where x is displacement and \(t\) is time in seconds. The maximum acceleration of the particle is \(\mathrm{x} \times 10^{-2} \mathrm{~ms}^{-2}\). The value of x is : 2025 Medium
18. 18. 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
19. 19. Two blocks of masses \(m\) and \(M,(M \gt m)\), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then
    (\(\mu=\) coefficient of friction between the two blocks)
    
    (A) The time period of small oscillation of the two blocks is \(\mathrm{T}=2 \pi \sqrt{\frac{(\mathrm{~m}+\mathrm{M})}{\mathrm{k}}}\)
    (B) The acceleration of the blocks is \(\mathrm{a}=\frac{\mathrm{kx}}{\mathrm{M}+\mathrm{m}}\) (\(\mathrm{x}=\) displacement of the blocks from the mean position)
    (C) The magnitude of the frictional force on the upper block is \(\frac{m \mu|x|}{M+m}\)
    (D) The maximum amplitude of the upper block, if it does not slip, is \(\frac{\mu(M+m) g}{k}\)
    (E) Maximum frictional force can be \(\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}\).
    Choose the correct answer from the options given below: 2025 Hard
20. 20. 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
21. 21. Two simple pendulums having lengths \(l_1\) and \(l_2\) with negligible string mass undergo angular displacements \(\theta_1\) and \(\theta_2\), from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct? 2025 Medium
22. 22. A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle \((\theta)\) of thread deflection in the extreme position will be : 2024 Hard
23. 23. A mass \(\mathrm{m}\) is suspended from a spring of negligible mass and the system oscillates with a frequency \(f_1\). The frequency of oscillations if a mass \(9 \mathrm{~m}\) is suspended from the same spring is \(f_2\). The value of \(\frac{f_1}{f_{.2}}\) is _______. 2024 Hard
24. 24. 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
25. 25. 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
26. 26. A particle of mass \(0.50 \mathrm{~kg}\) executes simple harmonic motion under force \(\mathrm{F}=-50\left(\mathrm{Nm}^{-1}\right) \mathrm{x}\). The time period of oscillation is \(\frac{x}{35} s\). The value of \(x\) is _______. (Given \(\pi=\frac{22}{7}\) ) 2024 Hard
27. 27. 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
28. 28. 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
29. 29. 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
30. 30. A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is \(4 \mathrm{~m}\), then the time period of small oscillations will be _______ \(s\). [take \(\mathrm{g}=\pi^2 \mathrm{~ms}^{-2}\)] 2024 Hard
31. 31. 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
32. 32. 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
33. 33. The bob of a pendulum was released from a horizontal position. The length of the pendulum is \(10 \mathrm{~m}\). If it dissipates \(10 \%\) of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is : _______. [Use, \(\mathrm{g}: 10 \mathrm{~ms}^{-2}\) ] 2024 Hard
34. 34. 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
35. 35. The length of a seconds pendulum at a height \(h=2 R\) from earth surface will be _______. (Given: \(R =\) Radius of earth and acceleration due to gravity at the surface of earth \(g =\pi^{2}\,m / s ^{-2}\) ) 2024 Medium
36. 36. The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of \(4 \mathrm{~m}, 2 \mathrm{~ms}^{-1}\) and \(16 \mathrm{~ms}^{-2}\) at a certain instant. The amplitude of the motion is \(\sqrt{\mathrm{x}} \mathrm{m}\) where \(\mathrm{x}\) is _______. 2024 Hard
37. 37. The time period of simple harmonic motion of mass \(\mathrm{M}\) in the given figure is \(\pi \sqrt{\frac{\alpha M}{5 K}}\), where the value of \(\alpha\) is _______.
    2024 Hard
38. 38. To find the spring constant \((k)\) of a spring experimentally, a student commits \(2 \%\) positive error in the measurement of time and \(1 \%\) negative error in measurement of mass. The percentage error in determining value of \(\mathrm{k}\) is _______. 2024 Hard
39. 39. 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
40. 40. A block of mass \(2\,kg\) is attached with two identical springs of spring constant \(20\,N / m\) each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is \(\frac{\pi}{\sqrt{x}}\) in SI unit. The value of \(x\) is \(..........\)
    2023 Medium
41. 41. A mass \(m\) attached to free end of a spring executes SHM with a period of \(1\; s\). If the mass is increased by \(3\; kg\) the period of oscillation increases by one second, the value of mass \(m\) is \(..............kg\). 2023 Medium
42. 42. A mass \(m\) is attached to two springs as shown in figure. The spring constants of two springs are \(K _1\) and \(K _2\). For the frictionless surface, the time period of oscillation of mass \(m\) is
    2023 Medium
43. 43. 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
44. 44. 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
45. 45. 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
46. 46. 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
47. 47. A particle of mass \(250\,g\) executes a simple harmonic motion under a periodic force \(F =(-25\,x) N\). The particle attains a maximum speed of \(4\,m / s\) during its oscillation. The amplitude of the motion is \(...........cm\). 2023 Medium
48. 48. A rectangular block of mass \(5\,kg\) attached to a horizontal spiral spring executes simple harmonic motion of amplitude \(1\,m\) and time period \(3.14\,s\). The maximum force exerted by spring on block is \(.......N\). 2023 Medium
49. 49. A simple pendulum with length \(100\,cm\) and bob of mass \(250\,g\) is executing S.H.M. of amplitude \(10\,cm\). The maximum tension in the string is found to be \(\frac{x}{40}\,N\). The value of \(x\) is \(..........\). 2023 Hard
50. 50. Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is \(100 g\). The time period of the motion of the particle will be (approximately) (take \(g =10\,ms ^{-2}\), radius of earth \(=6400\,km\) ) 2023 Medium

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