(C) The block is in simple harmonic motion. When the spring is at its natural length,the block is at the mean position,and its kinetic energy is maxim

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(C) The block is in simple harmonic motion. When the spring is at its natural length,the block is at the mean position,and its kinetic energy is maximum.At the mean position,the total energy is purely kinetic: $E = \frac{1}{2}mv^2$.At the extreme position,the block comes to an instantaneous rest,and the total energy is purely potential: $E = \frac{1}{2}kx^2$.By the law of conservation of mechanical energy,the total energy at the mean position equals the total energy at the extreme position:$\frac{1}{2}mv^2 = \frac{1}{2}kx^2$Solving for $x$:$x^2 = \frac{m}{k}v^2$$x = v\sqrt{\frac{m}{k}}$

Class 11 Physics Oscillations SHM of Spring Mass System

Easy

$A$ block of mass $m$,attached to a spring of spring constant $k$,oscillates on a smooth horizontal table. The other end of the spring is fixed to a wall. The block has a speed $v$ when the spring is at its natural length. Before coming to an instantaneous rest,if the block moves a distance $x$ from the mean position,then

A
$x = \sqrt{m/k}$
B
$x = \frac{1}{v} \sqrt{m/k}$
C
$x = v \sqrt{m/k}$
D
$x = \sqrt{mv/k}$

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SHM of Spring Mass System

$A$ block of mass $m$ is at rest on another block of the same mass as shown in the figure. The lower block is attached to a spring. What is the maximum amplitude of motion such that both blocks remain in contact?

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$A$ tray of mass $12 \,kg$ is supported by two identical springs as shown in the figure. When the tray is pressed down slightly and then released, it executes $SHM$ with a time period of $1.5 \,s$. The spring constant of each spring is

DifficultKCET 2020

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Two massless springs with spring constants $2k$ and $9k$ carry $50\,g$ and $100\,g$ masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then,the ratio of their respective amplitudes will be

MediumJEE MAIN 2022

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When a particle of mass $m$ is attached to a vertical spring of spring constant $k$ and released,its motion is described by $y(t) = y_{0} \sin^{2} \omega t$,where $y$ is measured from the lower end of the unstretched spring. Then $\omega$ is

DifficultJEE MAIN 2020

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$A$ mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $S.H.M.$ of time period $T$. If the mass is increased by $m$,the time period becomes $5T/3$. Then the ratio of $m/M$ is

MediumAIEEE 2003

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$A$ block of mass $m$ is at rest on another block of the same mass as shown in the figure. The lower block is attached to a spring. What is the maximum amplitude of motion such that both blocks remain in contact?

$A$ tray of mass $12 \,kg$ is supported by two identical springs as shown in the figure. When the tray is pressed down slightly and then released, it executes $SHM$ with a time period of $1.5 \,s$. The spring constant of each spring is

Two massless springs with spring constants $2k$ and $9k$ carry $50\,g$ and $100\,g$ masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then,the ratio of their respective amplitudes will be

When a particle of mass $m$ is attached to a vertical spring of spring constant $k$ and released,its motion is described by $y(t) = y_{0} \sin^{2} \omega t$,where $y$ is measured from the lower end of the unstretched spring. Then $\omega$ is

$A$ mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $S.H.M.$ of time period $T$. If the mass is increased by $m$,the time period becomes $5T/3$. Then the ratio of $m/M$ is

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