Oscillations (SHM) · JEE Main previous year questions

2024 16 questions

1. Q562024 · 9 Apr 2024 · Shift 1· Numerical answer

   The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4\text{ m}$, $2{\text{ ms}}^{-1}$ and $16{\text{ ms}}^{-2}$ at a certain instant. The amplitude of the motion is $\sqrt{x}\text{ m}$ where $x$ is ______.

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   Answer: 17

2. Q562024 · 9 Apr 2024 · Shift 2· Numerical answer

   A particle of mass $0.50\mathrm{kg}$ executes simple harmonic motion under force $F=-50({\mathrm{Nm}}^{-1})x$. The time period of oscillation is $\frac{x}{35}s$. The value of $x$ is ____. (Given $\pi =\frac{22}{7}$)

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   Answer: 22

3. Q552024 · 8 Apr 2024 · Shift 2· Numerical answer

   An object of mass $0.2\mathrm{kg}$ executes simple harmonic motion along $x$ axis with frequency of $\left(\frac{25}{\pi }\right)\mathrm{Hz}$. At the position $x=0.04\mathrm{m}$ the object has kinetic energy $0.5\mathrm{J}$ and potential energy $0.4\mathrm{J}$. The amplitude of oscillation is ____ $\mathrm{cm}$.

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   Answer: 6

4. Q552024 · 4 Apr 2024 · Shift 1· Numerical answer

   An elastic spring under tension of $3\mathrm{N}$ has a length $a$. Its length is $b$ under tension $2\mathrm{N}$. For its length $(3a-2b)$, the value of tension will be ____ $\mathrm{N}$.

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   Answer: 5

5. Q372024 · 4 Apr 2024 · Shift 2
   
   1. A.$E/\sqrt{2}$
   2. B.$2E$
   3. C.$E\sqrt{2}$
   4. D.$E$
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   Answer: D

6. Q592024 · 4 Apr 2024 · Shift 2· Numerical answer

   The displacement of a particle executing SHM is given by $x=10\sin \left(wt+\frac{\pi }{3}\right)m$. The time period of motion is $3.14\text{ s}$. The velocity of the particle at $t=0$ is ________ $\text{m/s}$.

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   Answer: 10

7. Q322024 · 1 Feb 2024 · Shift 1

   If $\mathrm{R}$ is the radius of the earth and the acceleration due to gravity on the surface of earth is $g={\pi }^{2}m/{\mathrm{s}}^2$, then the length of the second's pendulum at a height $\mathrm{h}=2R$ from the surface of earth will be :

   1. A.$\frac{1}{9}\mathrm{m}$
   2. B.$\frac{8}{9}\mathrm{m}$
   3. C.$\frac{2}{9}\mathrm{m}$
   4. D.$\frac{4}{9}\mathrm{m}$
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   Answer: A

8. Q452024 · 1 Feb 2024 · Shift 1

   A simple pendulum of length $1\mathrm{m}$ has a wooden bob of mass $1\mathrm{kg}$. It is struck by a bullet of mass $10^{-2}\mathrm{kg}$ moving with a speed of $2\times 10^2\mathrm{m}{\mathrm{s}}^{-1}$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use $\mathrm{g}=10m/{\mathrm{s}}^2$ )

   1. A.$0.20\mathrm{m}$
   2. B.$0.40\mathrm{m}$
   3. C.$0.30\mathrm{m}$
   4. D.$0.35\mathrm{m}$
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   Answer: A

9. Q512024 · 1 Feb 2024 · Shift 2· Numerical answer

   A mass $m$ is suspended from a spring of negligible mass and the system oscillates with a frequency $f_1$. The frequency of oscillations if a mass $9\text{ m}$ is suspended from the same spring is $f_2$. The value of $\frac{f_1}{f_2}$ is ________ .

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   Answer: 3

10. Q562024 · 31 Jan 2024 · Shift 1· Numerical answer

    A particle performs simple harmonic motion with amplitude $A$. Its speed is increased to three times at an instant when its displacement is $\frac{2A}{3}$. The new amplitude of motion is $\frac{nA}{3}$. The value of $n$ is ____.

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    Answer: 7

11. Q432024 · 31 Jan 2024 · Shift 2

    The measured value of the length of a simple pendulum is $20\mathrm{cm}$ with $2\mathrm{mm}$ accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is $\mathrm{N}\%$. The value of $\mathrm{N}$ is:

    1. A.6
    2. B.5
    3. C.4
    4. D.8
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    Answer: A

12. Q602024 · 31 Jan 2024 · Shift 2· Numerical answer
    
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    Answer: 12

13. Q582024 · 29 Jan 2024 · Shift 1· Numerical answer

    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 $x=$ _______.

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    Answer: 9

14. Q452024 · 29 Jan 2024 · Shift 2

    The bob of a pendulum was released from a horizontal position. The length of the pendulum is $10\text{ m}$. If it dissipates $10\%$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, $g:10{\text{ ms}}^{-2}$]

    1. A.$5\sqrt{6}{\text{ ms}}^{-1}$
    2. B.$5\sqrt{5}{\text{ ms}}^{-1}$
    3. C.$2\sqrt{5}{\text{ ms}}^{-1}$
    4. D.$6\sqrt{5}{\text{ ms}}^{-1}$
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    Answer: D

15. Q562024 · 29 Jan 2024 · Shift 2· Numerical answer

    A simple harmonic oscillator has an amplitude $A$ and time period $6\pi \text{ second}$. Assuming the oscillation starts from its mean position, the time required by it to travel from $x=\mathrm{A}$ to $x=\frac{\sqrt{3}}{2}\text{ A}$ will be $\frac{\pi }{x}\text{ s}$, where $x=$ _________.

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    Answer: 2

16. Q572024 · 27 Jan 2024 · Shift 1· Numerical answer

    A particle executes simple harmonic motion with an amplitude of $4\text{ cm}$. At the mean position, velocity of the particle is $10\text{ cm/s}$. The distance of the particle from the mean position when its speed becomes $5\text{ cm/s}$ is $\sqrt{\alpha }\text{ cm}$, where $\alpha =$ _______.

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    Answer: 12