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Standard XII

Physics

Defining Kinetic Energy

The phase spa...

Question

The phase space diagram for simple Momentum harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $E_{1}$ and $E_{2}$ are the total mechanical energies respectively. Then:

E_{1} = \sqrt{2} E_{2}

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E_{1} = 2 E_{2}

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E_{1} = 4 E_{2}

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E_{1} = 16 E_{2}

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Solution

The correct option is B $E_{1} = 4 E_{2}$
Since E is directly proportional to $A^{2}$
So, $\frac{E_{1}}{E_{2}} = \frac{A_{1}^{2}}{A_{2}^{2}}$
Therefore, $E_{1} = 4 E_{2}$

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The phase space diagram for simple Momentum harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and E1 and E2 are the total mechanical energies respectively. Then:

The correct option is B E1=4E2Since E is directly proportional to A2So, E1E2=A21A22Therefore, E1=4E2

The phase space diagram for simple Momentum harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $E_{1}$ and $E_{2}$ are the total mechanical energies respectively. Then:

The correct option is B $E_{1} = 4 E_{2}$
Since E is directly proportional to $A^{2}$
So, $\frac{E_{1}}{E_{2}} = \frac{A_{1}^{2}}{A_{2}^{2}}$
Therefore, $E_{1} = 4 E_{2}$