Two identical springs of spring constant k are attached to a block of mass m and to fixed supports a

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13.Oscillations

easy

Two identical springs of spring constant $k$ are attached to a block of mass $m$ and to fixed supports as shown in Figure. Show that when the mass is displaced from its equilibrium position on either side, it executes a simple harmonic motion. Find the period of oscillations.

Option A

Option B

Option C

Option D

Solution

Let the mass be displaced by a small distance x to the right side of the equilibrium position, as shown in Figure. Under this situation the spring on the left side gets elongated by a length equal to $x$ and that on the right side gets compressed by the same length. The forces acting on the mass are then,

$F_{1}=-k x$ (force exerted by the spring on the left side, trying to pull the mass towards the mean position

$F_{2}=-k x$ (force exerted by the spring on the right side, trying to push the mass towards the mean position)

The net force, $F$, acting on the mass is then given by,

$F=-2 k x$

Hence the force acting on the mass is proportional to the displacement and is directed towards the mean position; therefore, the motion executed by the mass is simple harmonic. The time period of oscillations is,

$T=2 \pi \sqrt{\frac{m}{2 k}}$

Standard 11

Physics

One end of a spring of force constant k is fixed to a vertical wall and the other to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance ${x_0}$ from the black. The spring is then compressed by $2{x_0}$ and released. The time taken to strike the wall is

hard

The graph shown was obtained from experimental measurements of the period of oscillations $T$ for different masses $M$ placed in the scale pan on the lower end of the spring balance. The most likely reason for the line not passing through the origin is that the

easy

If a spring has time period $T$, and is cut into $n$ equal parts, then the time period of each part will be

easy

(AIEEE-2002)

The scale of a spring balance reading from $0$ to $10 \,kg$ is $0.25\, m$ long. A body suspended from the balance oscillates vertically with a period of $\pi /10$ second. The mass suspended is ….. $kg$ (neglect the mass of the spring)

medium

$A$ block of mass $M_1$ is hanged by a light spring of force constant $k$ to the top bar of a reverse Uframe of mass $M_2$ on the floor. The block is pooled down from its equilibrium position by $a$ distance $x$ and then released. Find the minimum value of $x$ such that the reverse $U$ -frame will leave the floor momentarily.

medium

Two identical springs of spring constant $k$ are attached to a block of mass $m$ and to fixed supports as shown in Figure. Show that when the mass is displaced from its equilibrium position on either side, it executes a simple harmonic motion. Find the period of oscillations.

Solution

Similar Questions

One end of a spring of force constant k is fixed to a vertical wall and the other to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance ${x_0}$ from the black. The spring is then compressed by $2{x_0}$ and released. The time taken to strike the wall is

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