B Why is a simple pendulum not a perfect simple harmonic oscillator?

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A simple pendulum is not a perfect simple harmonic oscillator because its restoring force is not directly proportional to the angle of displacement, especially at larger angles. As the angle increases, the approximation of the restoring torque deviates from the ideal linear relationship. This leads to variations in the period of the pendulum, which can be better approximated using more complex formulas. In contrast, Christiaan Huygens's pendulum, which follows the tautochrone curve, maintains a constant period regardless of amplitude, qualifying it as a true simple harmonic oscillator. Understanding these distinctions is crucial for accurate physics modeling.
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Khan Academy claims that a simple pendulum not a perfect simple harmonic oscillator. Why is it so?
 
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Huzaifa said:
Khan Academy claims that a simple pendulum not a perfect simple harmonic oscillator. Why is it so?
Is the restoring torque exactly proportional to the angle of the pendulum? What happens if the angle gets big?
 
Because the restoring force is not exactly (negatively) proportional to the displacement.
 
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Yes, the simple pendulum is not a simple harmonic oscillator for reasons already explained. However, Christiaan Huygens's pendulum follows the tautochrone curve which is not as simple as a circle but has amplitude-independent period, i.e. is a simple harmonic oscillator.
 
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Thread 'The rocket equation, one more time'

Thread 'The rocket equation, one more time'

I already posted a similar thread a while ago, but this time I want to focus exclusively on one single point that is still not clear to me. I just came across this problem again in Modern Classical Mechanics by Helliwell and Sahakian. Their setup is exactly identical to the one that Taylor uses in Classical Mechanics: a rocket has mass m and velocity v at time t. At time ##t+\Delta t## it has (according to the textbooks) velocity ##v + \Delta v## and mass ##m+\Delta m##. Why not ##m -...
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