Spring Force

When, two ends of an ideal spring are pulled apart increasing its length it produces force equal to $kx$ at its ends. At a point $\frac{1}{4}$ of its length from one end, the force is

Two blocks $A\&B$ with mass $4 \mathrm{kg}$ and $6 \mathrm{kg}$ respectively are connected by a stretched spring of negligible mass as in figure. When the two blocks are released simultaneously the initial acceleration of $B$ is $1.5 \mathrm{m}/{\mathrm{s}}^2$ westward. The acceleration of $A$ is:

Two springs of force constants $300 \mathrm{N}/\mathrm{m}$ (Spring A) and $400 \mathrm{N}/\mathrm{m}$ (Spring B) are joined together in series. The combination is compressed by $8.75 \mathrm{cm}$. The ratio of energy stored in $\mathrm{A}$ and $\mathrm{B}$ is $\frac{{\mathrm{E}}_{\mathrm{A}}}{{\mathrm{E}}_{\mathrm{B}}}.$ Then $\frac{{\mathrm{E}}_{\mathrm{A}}}{{\mathrm{E}}_{\mathrm{B}}}$ is equal to:

In a $\mathrm{HCl}$ molecule, the $\mathrm{Cl}$ can be treated on infinite mass and $\mathrm{H}$ oscillating alone. If the oscillation of $\mathrm{HCl}$ molecule shows frequency of $7\times {10}^{13} {\mathrm{s}}^{-1}\text{,}$ the value of force constant is (take Avogadro number$=6\times {10}^{26} \mathrm{per} \mathrm{kg}-\mathrm{mole})$

The system shown in the figure is released from rest. Pulley and spring are massless and friction is absent everywhere. The speed of $5 \mathrm{kg}$ block when $2 \mathrm{kg}$ block leaves the contact with ground is $\left(K=40 \mathrm{N} {\mathrm{m}}^{-1} \& \mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A mass $m$ is suspended by two springs of force constants $K_1$ and $K_2$ respectively as shown in the diagram. The total elongation (stretch) of the two springs is

What will be time period of the displaced body of mass $m$ ?

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

A solid cylinder of mass $3 \mathrm{kg}$ is rolling on a horizontal smooth surface with velocity $4m{s}^{-1}$. It strikes with a fixed horizontal spring of force constant $200N{m}^{-1}$ . The maximum compression produced in the spring 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:

In the system shown in figure $M_1>M_2$ and pulley and threads are ideal. System is held at rest by thread $BC.$ Just after thread $BC$ is burnt,

Two springs are connected to a block of mass $M$ placed on a frictionless surface as shown below. If both the springs have a spring constant $k,$ then the frequency of oscillation of the block is

Two identical springs (spring constant = $k$) are connected to two light rigid rods in parallel combination and then a third spring (identical to the other two) is connected to this combination in series. The combined system is fixed to the ceiling and a block of mass $m$ is attached as shown in the figure. If the mass is slightly displaced and then let go, then the system shall oscillate with a time period of

Consider a system of two solid balls connect by a light spring in air which is horizontal at the given instant. The horizontal acceleration of the 10 kg ball is $12 m/s^2$ towards right at the given instant. What would be the total acceleration of the 20 kg ball, if it starts falling? (take $g= 10m/s^2$ )

As shown in figure a simple harmonic motion oscillator having identical four springs has time period

If ${\mathrm{k}}_{\mathrm{s}}$ and ${\mathrm{k}}_{\mathrm{p}}$ respectively are effective spring constant in series and parallel combination of springs as shown in figure, find $\frac{{\mathrm{k}}_{\mathrm{s}}}{{\mathrm{k}}_{\mathrm{p}}}$

A particle of mass $m$ is attached to three identical springs $\mathrm{A}$, $\mathrm{B}$ and $\mathrm{C}$ each of force constant $k$ as shown in figure. If the particle of mass $m$ is pushed slightly against the spring $\mathrm{A}$ and released then the time period of oscillations is

On a smooth inclined plane, a body of mass M is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant K, the period of oscillation of the body (assuming the springs as massless) is

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of