The curve between the potential energy $$(U)$$ and displacement $$(x)$$ is shown. Which of the oscillation is about the mean position, $$x = 0?$$

 1 2 3 4
Subtopic:  Energy of SHM |
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A particle of mass m oscillates with simple harmonic motion between points x1 and x2, the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph:

 1 2 3 4
Subtopic:  Energy of SHM |
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AIPMT - 2003
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Equation of a simple harmonic motion is  given by x = asin$\mathrm{\omega }$t. For which value of x, kinetic energy is equal to the potential energy?

1.  $\mathrm{x}$ $=$ $±$ $\mathrm{a}$

2.  $\mathrm{x}$ $=$ $±$ $\frac{\mathrm{a}}{2}$

3.  $\mathrm{x}$ $=$ $±$ $\frac{\mathrm{a}}{\sqrt{2}}$

4.  $\mathrm{x}$ $=$ $±$ $\frac{\sqrt{3}\mathrm{a}}{2}$

Subtopic:  Energy of SHM |
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When the displacement is half the amplitude in an SHM, the ratio of potential energy to the total energy is:
1. 1 / 2

2. 1 / 4

3. 1

4. 1 / 8

Subtopic:  Energy of SHM |
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The potential energy of a simple harmonic oscillator, when the particle is halfway to its endpoint, will be:
1. $$\frac{2E}{3}$$
2. $$\frac{E}{8}$$
3. $$\frac{E}{4}$$
4. $$\frac{E}{2}$$

Subtopic:  Energy of SHM |
79%
From NCERT
AIPMT - 2003
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The kinetic energy (K) of a simple harmonic oscillator varies with displacement (x) as shown. The period of the oscillation will be: (mass of oscillator is 1 kg)

 1 $\frac{\mathrm{\pi }}{2}$ sec 2 $\frac{1}{2}$ sec 3 $\mathrm{\pi }$ sec 4 1 sec
Subtopic:  Energy of SHM |
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A block of mass $$4~\text{kg}$$ hangs from a spring of spring constant $$k = 400~\text{N/m}$$. The block is pulled down through $$15~\text{cm}$$ below the equilibrium position and released. What is its kinetic energy when the block is $$10~\text{cm}$$ below the equilibrium position? [Ignore gravity]
1. $$5~\text{J}$$
2. $$2.5~\text{J}$$
3. $$1~\text{J}$$
4. $$1.9~\text{J}$$

Subtopic:  Energy of SHM |
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Kinetic energy of a particle executing simple harmonic motion in straight line is $$pv^2$$ and potential energy is $$qx^2,$$ where $$v$$ is speed at distance $$x$$ from the mean position. The time period of the SHM is given by the expression:

1. $2\mathrm{\pi }\sqrt{\frac{\mathrm{q}}{\mathrm{p}}}$

2. $2\mathrm{\pi }\sqrt{\frac{p}{q}}$

3. $2\mathrm{\pi }\sqrt{\frac{\mathrm{q}}{\mathrm{p}+\mathrm{q}}}$

4. $2\mathrm{\pi }\sqrt{\frac{p}{p+q}}$

Subtopic:  Energy of SHM |
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The total energy of a particle, executing simple harmonic motion is:

1. $\propto$ $x$

2. $\propto$ ${x}^{2}$

3.  Independent of x

4.  $\propto$ ${x}^{1/2}$

Subtopic:  Energy of SHM |
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A particle executes SHM with a frequency of $$20$$ Hz. The frequency with which its potential energy oscillates is:
1. $$5$$ Hz
2. $$20$$ Hz
3. $$10$$ Hz
4. $$40$$ Hz

Subtopic:  Energy of SHM |
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