Oscillations (SHM) · JEE Main previous year questions

2025 7 questions

1. Q282025 · 4 Apr 2025 · Shift 1

   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?

   1. A.${\theta }_1{l}_2={\theta }_2{l}_1$
   2. B.${\theta }_1{l}_1={\theta }_2{l}_2$
   3. C.${\theta }_1{l}_2^2={\theta }_2{l}_1^2$
   4. D.${\theta }_1{l}_1^2={\theta }_2{l}_2^2$
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   Answer: A

2. Q402025 · 3 Apr 2025 · Shift 1
   
   1. A.B, C, D Only
   2. B.C, D, E Only
   3. C.A, B, D Only
   4. D.A, B, C Only
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   Answer: C

3. Q342025 · 2 Apr 2025 · Shift 1

   A particle is subjected to two simple harmonic motions as : $x_1=\sqrt{7}\sin 5t\text{ cm}$ and $x_2=2\sqrt{7}\sin \left(5t+\frac{\pi }{3}\right)\text{cm}$ where $x$ is displacement and $t$ is time in seconds. The maximum acceleration of the particle is $x\times 10^{-2}{\text{ ms}}^{-2}$. The value of $x$ is :

   1. A.$5\sqrt{7}$
   2. B.125
   3. C.$25\sqrt{7}$
   4. D.175
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   Answer: D

4. Q272025 · 2 Apr 2025 · Shift 2

   In a moving coil galvanometer, two moving coils ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ have the following particulars : ${\mathrm{R}}_1=5\Omega$, ${\mathrm{N}}_1=15$, ${\mathrm{A}}_1=3.6\times 10^{-3}{\mathrm{m}}^2$, ${\mathrm{B}}_1=0.25\mathrm{T}$ ${\mathrm{R}}_2=7\Omega$, ${\mathrm{N}}_2=21$, ${\mathrm{A}}_2=1.8\times 10^{-3}{\mathrm{m}}^2$, ${\mathrm{B}}_2=0.50\mathrm{T}$ Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of $M_1$ and $M_2$ ?

   1. A.$1:1$
   2. B.$1:3$
   3. C.$1:2$
   4. D.$1:4$
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   Answer: A

5. Q352025 · 29 Jan 2025 · Shift 2

   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

   1. A.$\sqrt{\frac{k_2}{k_1}}$
   2. B.$\sqrt{\frac{k_1}{k_2}}$
   3. C.$\frac{k_2}{k_1}$
   4. D.$\frac{k_1}{k_2}$
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   Answer: B

6. Q322025 · 24 Jan 2025 · Shift 1

   A particle is executing simple harmonic motion with time period $2\mathrm{s}$ and amplitude $1\mathrm{cm}$ . If $\mathrm{D}$ and $\mathrm{d}$ are the total distance and displacement covered by the particle in $12.5\mathrm{s}$ , then $\frac{\mathrm{D}}{\mathrm{d}}$ is

   1. A.$10$
   2. B.$\frac{16}{5}$
   3. C.$25$
   4. D.$\frac{15}{4}$
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   Answer: C

7. Q292025 · 23 Jan 2025 · Shift 2

   A massless spring gets elongated by amount $x_1$ under a tension of $5\text{ N}$ . Its elongation is $x_2$ under the tension of $7\text{ N}$ . For the elongation of $(5x_1-2x_2)$, the tension in the spring will be,

   1. A.$20\text{ N}$
   2. B.$39\text{ N}$
   3. C.$11\text{ N}$
   4. D.$15\text{ N}$
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   Answer: C