# Questions tagged [approximations]

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### Why does a simple pendulum or a spring-mass system show simple harmonic motion only for small amplitudes?

I've been taught that in a simple pendulum, for small $x$, $\sin x \approx x$. We then derive the formula for the time period of the pendulum. But I still don't understand the Physics behind it. Also, ...
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### Tidal force formula

My book explains what happens if we measure the difference in gravitational force by displacing a test mass by $\Delta r\ll r$. They give the following formula: $$\Delta F=\frac{2GMm\Delta r}{r^3}.$$...
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### Planck's theory question

Could you please tell me why Planck's theory ceases to be valid when the sizes of the bodies and/or their separation distances are comparable to, or smaller than, the wavelength. My professor told me ...
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### Idealizations of an object as a point particle

Why is it that an object can be idealized as a point particle or 'particle like' to solve problems? What are the limits of such a tool?
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### Velocity between two running animals

One animal $A$ can run $100$ km/h and another animal $B$ can run $85$ km/h. Suppose the slower animal $B$ starts running $25$ meters ahead of the faster animal $A$ in a direction. How can I ...