Oscillations of a Spring - Block System

A block of mass $\mathrm{M}$ is placed on a smooth horizontal surface, and it is pulled by a light spring as shown in the diagram. If the ends $\mathrm{A}$ and $\mathrm{B}$ of the spring are moving with $4 \mathrm{m} {\mathrm{s}}^{-1}$ and $2 \mathrm{m} {\mathrm{s}}^{-1}$ respectively in the same direction and at this moment the rate at which spring energy is increasing is $20 \mathrm{J} {\mathrm{s}}^{-1}$, then what is the value of spring force (in $\mathrm{N}$)?

A mass of $0.2 \mathrm{kg}$ is attached to the lower end of a massless spring of force constant $200 \mathrm{N} {\mathrm{m}}^{-1}$, the upper end of which is fixed to a rigid support. Which of the following statement is true?

An arrangement of spring, strings, pulley and masses is shown in the figure below.

The pulley and the strings are massless and $M>m$. The spring is light with spring constant $k$. If the string connecting $m$ to the ground is detached, then immediately after detachment

Two blocks of masses $m$ and $M$ are moving with speed $v_1$ and $v_2\left(v_1>v_2\right)$ in the same direction on the frictionless surface respectively, $M$ being ahead of $m$. An ideal spring of force constant $k$ is attached to the backside of $M$ (as shown). The maximum compression of the spring when the blocks collide is 

Angular frequency in SHM is given by $\text{ω}=\sqrt{\frac{\text{k}}{\text{m}}}$. Maximum acceleration in SHM is ${\text{ω}}^{2}A$ and maximum value of friction between two bodies in contact is $\text{μ}\text{N}$, where N is the normal reaction between the bodies.
  Now the value of k, the force constant is increased, then the maximum amplitude calculated in above question will

Electrostatic force on a charged particle is given by $\overrightarrow{\text{F}}=\text{q}\overrightarrow{\text{E}}$. If q is positive $\overrightarrow{\text{F}}\uparrow \uparrow \overrightarrow{\text{E}}$ and if q negative $\overrightarrow{\text{F}}\uparrow \downarrow \overrightarrow{\text{E}}$

In the figure m_A = m_B = 1 kg. Block A is neutral while q_B = - 1C. Sizes of A and B are negligible. B is released from rest at a distance 1.8 m from A. Initially  spring is neither compressed nor elongated.

Equilibrium position of the combined mass is at $x = ........m$

At the instant speed of block is maximum, the magnitude of force exerted by spring on the block is:

Let $k$ be the spring constant of a spring. If the spring is cut into two equal parts, then spring constant of each part is

The time period of mass $M$ when displaced from its equilibrium position and then released for the system as shown in figure is

Match the Column I with Column II:

	Column - I		Column - II
$\left(\mathrm{a}\right)$		$\left(\mathrm{i}\right)$	$T=2\mathrm{\pi }\sqrt{\frac{m\left(k_1+k_2\right)}{k_1{k}_2}}$
$\left(\mathrm{b}\right)$		$\left(\mathrm{i}\mathrm{i}\right)$	$T=2\mathrm{\pi }\sqrt{\frac{2\mathit{ }m}{k}}$
$\left(\mathrm{c}\right)$		$\left(\mathrm{i}\mathrm{i}\mathrm{i}\right)$	$T=2\mathrm{\pi }\sqrt{\frac{m}{2\mathit{ }k}}$
$\left(\mathrm{d}\right)$		$\left(\mathrm{i}\mathrm{v}\right)$	$T=2\mathrm{\pi }\sqrt{\frac{m}{k_1+k_2}}$

A trolley of mass $3\mathrm{ }\mathrm{k}\mathrm{g}$, as shown in figure, is connected to two identical springs, each having spring constant equal to $600\mathrm{ }\mathrm{N} {\mathrm{m}}^{-1}$. If the trolley is displaced from its equilibrium position by $5\mathrm{ }\mathrm{c}\mathrm{m}$ and released, the maximum speed of the trolley is:

A spring balance has a scale that reads from $0$ to $50\mathrm{ }\mathrm{k}\mathrm{g}$. The length of the scale is $20\mathrm{ }\mathrm{c}\mathrm{m}$. A block of mass $\mathrm{m}$ is suspended from this balance, displaced from its mean position and released, it oscillates with a period $0.5\mathrm{ }\mathrm{s}$. The value of $\mathrm{m}$ is (Take $g=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$)

Two blocks each of mass $m$, kept on smooth surface, are connected by a spring of spring constant $k$ as shown in the figure.

If the blocks are displaced slightly in opposite directions and released, they will execute simple harmonic motion. The time period of oscillation is

Natural length of the spring is $40\mathrm{ }\mathrm{c}\mathrm{m}$ and its spring constant is $4000\mathrm{ }\mathrm{N}\mathrm{ }{\mathrm{m}}^{-1}.$ A mass of $20\mathrm{ }\mathrm{k}\mathrm{g}$ is hung from it. The extension produced in the spring is
(Given $\mathrm{ }\mathrm{g}\mathrm{ }=9.8\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}$ )

A spring having a spring constant of $1200 \mathrm{N} {\mathrm{m}}^{-1}$, is mounted on a horizontal table, as shown in the figure. A mass of $3 \mathrm{kg}$ is attached to the free end of the spring. Then, the mass is pulled sideways to a distance of $2.0 \mathrm{cm}$ and released. Determine the maximum acceleration of the mass, and the maximum speed of the mass.

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A solid copper sphere is suspended from a massless spring. The time period of oscillation of the system is 4 second. The sphere is now completely immersed in a liquid whose density is 1/8 th that of brass. The sphere remains in liquid during oscillation. Now the time period is