Physics: A swinging pendulum has a total energy of . The amplitude of the pendulum s oscillations is then increased by a factor of 4. By what factor does the total energy stored in the moving pendulum change? Ignore damping.

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A swinging pendulum has a total energy of . The

Ответ:

olivasm5626

24.01.2022

Physics

$\frac{E_{2}}{E_{1}} \approx 1 -\frac{3\theta}{1-\theta}$ (for small oscillations)

Explanation:

The total energy of the pendulum is equal to:

$E_{1} = m\cdot g \cdot (1-\cos \theta)\cdot L$

For small oscillations, the equation can be re-arranged into the following form:

$E_{1} \approx m\cdot g \cdot (1-\theta) \cdot L$

Where:

$\theta = \frac{A}{L^{2}}$ , measured in radians.

If the amplitude of pendulum oscillations is increase by a factor of 4, the angle of oscillation is $4\theta$ and the total energy of the pendulum is:

$E_{2} \approx m\cdot g \cdot (1-4\theta)\cdot L$

The factor of change is:

$\frac{E_{2}}{E_{1}} \approx \frac{1 - 4\theta}{1-\theta}$

$\frac{E_{2}}{E_{1}} \approx 1 -\frac{3\theta}{1-\theta}$

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A swinging pendulum has a total energy of . The amplitude of the pendulum's oscillations is then increased by a factor of 4. By what factor does the total energy stored in the moving pendulum change? Ignore damping.

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