Question

 A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period $T_1$ and (ii) back and forth in a direction perpendicular to its plane, with a period $T_2$. The ratio $\frac{T_1}{T_2}$ will be :

JEE Main 2020 (05 Sep Shift 2)

Options

• A: $\frac{2}{\sqrt{3}}$
• B: $\frac{2}{3}$
• C: $\frac{3}{\sqrt{2}}$
• D: $\frac{\sqrt{2}}{3}$

Question

An object of mass $\mathrm{m}$ is suspended at the end of a massless wire of length $\mathrm{L}$ and area of cross-section, A. Young modulus of the material of the wire is $Y$. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is :

JEE Main 2020 (06 Sep Shift 1)

Options

• A: $f=\frac{1}{2\pi }\sqrt{\frac{mL}{YA}}$
• B: $f=\frac{1}{2\pi }\sqrt{\frac{YA}{mL}}$
• C: $f=\frac{1}{2\pi }\sqrt{\frac{mA}{VL}}$
• D: $f=\frac{1}{2\pi }\sqrt{\frac{YL}{mA}}$

Question

A mass of $5 \mathrm{kg}$ is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length $4 \mathrm{m}$ has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed ?

JEE Main 2021 (01 Sep Shift 2)

Options

• A: $4 \mathrm{m} {\mathrm{s}}^{-2}$
• B: $8 \mathrm{m} {\mathrm{s}}^{-2}$
• C: $5 \mathrm{m} {\mathrm{s}}^{-2}$
• D: $10 \mathrm{m} {\mathrm{s}}^{-2}$

Question

A particle is making simple harmonic motion along the $X$-axis. If at a distances $x_1$ and $x_2$ from the mean position the velocities of the particle are $v_1$ and $v_2$, respectively. The time period of its oscillation is given as:

JEE Main 2021 (20 Jul Shift 2)

Options

• A: $T=2\pi \sqrt{\frac{x_2^2+x_1^2}{v_1^2-v_2^2}}$
• B: $T=2\pi \sqrt{\frac{{\mathrm{x}}_2^2+{\mathrm{x}}_1^2}{v_1^2+v_2^2}}$
• C: $T=2\pi \sqrt{\frac{x_2^2-x_1^2}{v_1^2+v_2^2}}$
• D: $T=2\pi \sqrt{\frac{x_2^2-x_1^2}{v_1^2-v_2^2}}$

Question

In the given figure, a body of mass $M$ is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant $k,$ the frequency of oscillation of given body is:

JEE Main 2021 (24 Feb Shift 2)

Options

• A: $\frac{1}{2\pi }\sqrt{\frac{2k}{Mg\sin \alpha }}$
• B: $\frac{1}{2\pi }\sqrt{\frac{k}{Mg}\sin \alpha }$
• C: $\frac{1}{2\pi }\sqrt{\frac{k}{2M}}$
• D: $\frac{1}{2\pi }\sqrt{\frac{2k}{M}}$

Question

The point $A$ moves with a uniform speed along the circumference of a circle of radius $0.36 \mathrm{m}$ and covers $30°$ in $0.1 \mathrm{s}$. The perpendicular projection $P$ from $A$ on the diameter $MN$ represents the simple harmonic motion of $P$. The restoration force per unit mass when $P$ touches $M$ will be :

JEE Main 2021 (25 Feb Shift 2)

Options

• A: $0.49 \mathrm{N}$
• B: $9.87 \mathrm{N}$
• C: $50 \mathrm{N}$
• D: $100 \mathrm{N}$

Question

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.

The potential energy $U\left(x\right)$ versus time $\left(t\right)$ plot of the particle is correctly shown in figure:

JEE Main 2021 (27 Aug Shift 1)

Options

• A:
• B:
• C:
• D:

Question

Consider two identical springs each of spring constant $k$ and negligible mass compared to the mass $M$ as shown. Fig. $1$ shows one of them and Fig. $2$ shows their series combination. The ratios of time period of oscillation of the two SHM is $\frac{T_b}{T_a}=\sqrt{x},$ where value of $x$ is ______.

(Round off to the Nearest Integer)

JEE Main 2021 (17 Mar Shift 1)

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Question

Two simple harmonic motion, are represented by the equations

$y_1=10\sin \left(3\pi t+\frac{\pi }{3}\right); y_2=5(\sin 3\pi t+\sqrt{3}\cos 3\pi t)$

Ratio of amplitude of $y_1$ to $y_2=x:1$. The value of $x$ is

JEE Main 2021 (27 Aug Shift 2)

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Question

The potential energy of a particle of mass $4 \mathrm{kg}$ in motion along the $x$-axis is given by $\mathrm{U}=4\left(1-\cos 4\mathrm{x}\right) \mathrm{J}$. The time period of the particle for small oscillation $\left(\sin \theta \simeq \theta \right)$ $\left(\frac{\pi }{\mathrm{K}}\right) \mathrm{s}$. The value of $K$ is _____ .

JEE Main 2022 (28 Jul Shift 2)

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Question

A particle executes simple harmonic motion between $x=–A \text{and} x=+A$. If time taken by particle to go from $x = 0$ to $\frac{A}{2}$ is $2 \mathrm{s}$; then time taken by particle in going from $x=\frac{A}{2}$ to $A$ is:

JEE Main 2023 (25 Jan Shift 2)

Options

• A: $3 \mathrm{s}$
• B: $2 \mathrm{s}$
• C: $1.5 \mathrm{s}$
• D: $4 \mathrm{s}$

Question

For particle $P$ revolving round the centre $O$ with radius of circular path $r$ and regular velocity $\omega$, as shown in below figure, the projection of $OP$ on the $x$-axis at time $t$ is

JEE Main 2023 (08 Apr Shift 2)

Options

• A: $x\left(t\right)=r \cos \left(\omega t-\frac{\pi }{6}\right)$
• B: $x\left(t\right)=r \cos \left(\omega t+\frac{\pi }{6}\right)$
• C: $x\left(t\right)=r \sin \left(\omega t+\frac{\pi }{6}\right)$
• D: $x\left(t\right)=r \cos \left(\omega t\right)$

Question

In the figure given below. a block of mass $M=490 \mathrm{g}$ placed on a frictionless table is connected with two springs having same spring constant ($K=2 \mathrm{N} {\mathrm{m}}^{-1}$). If the block is horizontally displaced through $X$ $\mathrm{m}$ then the number of complete oscillations it will make in $14\pi$ seconds will be ______.

JEE Main 2023 (31 Jan Shift 1)

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Question

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 $\sqrt{x}, \mathrm{~m}$ where $x$ is ________

JEE Main 2024 (09 Apr Shift 1)

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Question

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 _____.

JEE Main 2024 (31 Jan Shift 1)

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Question

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 _________$\mathrm{s}$.

$[$take $g={\pi }^2 \mathrm{m} {\mathrm{s}}^{-2}$]

JEE Main 2024 (30 Jan Shift 2)

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