Oscillations (SHM) · JEE Main previous year questions

2026 13 questions

1. Q282026 · 8 Apr 2026 · Shift 2

   A car moving with a speed of $54km/h$ takes a turn of radius $20\mathrm{m}$. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take $g=10m/{\mathrm{s}}^2$)

   1. A.${\tan }^{-1}(0.5)$
   2. B.${\tan }^{-1}(0.75)$
   3. C.${\tan }^{-1}(1.125)$
   4. D.${\tan }^{-1}(0.25)$
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   Answer: C

2. Q372026 · 8 Apr 2026 · Shift 2

   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 ____ .

   1. A.$1$
   2. B.$2$
   3. C.$\sqrt{2}$
   4. D.$\sqrt{3}$
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   Answer: C

3. Q372026 · 6 Apr 2026 · Shift 1

   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 $x=\frac{A}{\sqrt{2}}$ is ____ $\sec$.

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

4. Q362026 · 6 Apr 2026 · Shift 2

   A spring stretches by $2\text{ mm}$ when it is loaded with a mass of $200\text{ g}$. From equilibrium position the mass is further pulled down by $2\text{ mm}$ and released. The frequency associated with the system and maxmimum energy in the spring are ________ $\text{Hz}$ and ________ $\text{J}$, respectively. (Take $g=10{\text{ m/s}}^2$)

   1. A.$\frac{5\sqrt{50}}{\pi }$ and $8\times 10^{-3}$
   2. B.$\frac{5\sqrt{50}}{\pi }$ and $8$
   3. C.$10\sqrt{50}$ and $2\times 10^{-3}$
   4. D.$\frac{5\sqrt{50}}{\pi }$ and $16\times 10^{-3}$
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   Answer: A

5. Q352026 · 5 Apr 2026 · Shift 2

   Match List - I with List - II. $$\begin{array}{ll}\text{List - I}& \text{List - II}\\ \text{A. }{\sin }^2\omega t& \text{I. Periodic with time period }T=\frac{\pi }{\omega }\text{ but not simple harmonic motion (SHM)}\\ \text{B. }{\sin }^3(2\omega t)& \text{II. Periodic with time period }T=\frac{2\pi }{\omega }\text{ but Not SHM}\\ \text{C. }\sin (\omega t)+\cos (\pi \omega t)& \text{III. Periodic with time period }T=\frac{\pi }{\omega }\text{ and SHM}\\ \text{D. }\cos \omega t+\cos 2\omega t& \text{IV. Non-periodic}\end{array}$$ Choose the correct answer from the options given below :

   1. A.A-III, B-I, C-IV, D-II
   2. B.A-II, B-I, C-III, D-IV
   3. C.A-III, B-II, C-IV, D-I
   4. D.A-II, B-I, C-IV, D-III
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   Answer: A

6. Q482026 · 4 Apr 2026 · Shift 1· Numerical answer

   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 $\frac{x}{7}\text{ s}$, the value of $x$ is ________.

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   Answer: 44

7. Q362026 · 4 Apr 2026 · Shift 2

   A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field ${\vec{\mathrm{E}}}_1={\mathrm{E}}_0\hat{x}$. If another electric field ${\vec{\mathrm{E}}}_2=2{\mathrm{E}}_0(\hat{y}+\hat{z})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

   1. A.$73\%$
   2. B.$63\%$
   3. C.$83\%$
   4. D.$53\%$
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   Answer: A

8. Q472026 · 28 Jan 2026 · Shift 1· Numerical answer

   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 ____ .

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   Answer: 2

9. Q282026 · 28 Jan 2026 · Shift 2

   The time period of a simple harmonic oscillator is $T=2\pi \sqrt{\frac{k}{m}}$. Measured value of mass ($m$) of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant ($k$) is ________%.

   1. A.3.43
   2. B.7.60
   3. C.3.35
   4. D.6.76
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   Answer: D

10. Q302026 · 24 Jan 2026 · Shift 1

    A spring of force constant $15N/m$ is cut into two pieces. If the ratio of their length is $1:3$, then the force constant of smaller piece is ____ N/m.

    1. A.20
    2. B.45
    3. C.60
    4. D.15
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    Answer: C

11. Q262026 · 23 Jan 2026 · Shift 1

    A simple pendulum of string length 30 cm performs 20 oscillations in 10 s . 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.]

    1. A.0.75
    2. B.7.5
    3. C.15
    4. D.120
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    Answer: B

12. Q462026 · 23 Jan 2026 · Shift 1· Numerical answer

    A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T . The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of $60^{\circ }$ with vertical, then maximum induced EMF between the point of suspension and point of oscillation is ____ mV . (Take $g=10{\text{ m/s}}^2$ )

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    Answer: 100

13. Q342026 · 21 Jan 2026 · Shift 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. [ take $\pi =\frac{22}{7}$ ]

    1. A.88
    2. B.14
    3. C.28
    4. D.176
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    Answer: B