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Suppose I have two pendulums:

1) a 400g bob, a 40cm arm

2) a 200g bob, a 20cm arm

Would the two have the same pendulum effect (time period/frequency), since the bob and the arm of 2) are half of 1)?

Any thought appreciated.

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  • $\begingroup$ What do you understand by the pendulum effect? $\endgroup$ – Gert Nov 21 '16 at 1:48
  • $\begingroup$ @Gert I mean the frequency. My understanding is that the equation is $T=2\pi\times\sqrt(\frac{L}{g})$. Does that mean the weight of the bob has no effect whatsoever on the frequency? $\endgroup$ – John M. Nov 21 '16 at 2:28
  • $\begingroup$ Yes, the mass of the bob has no effect on frequency! Fact. en.wikipedia.org/wiki/Pendulum#Period_of_oscillation $\endgroup$ – Gert Nov 21 '16 at 2:36
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The mass had no effect on the frequency/time period. However, if length is halved, frequency becomes $\sqrt{2}$ times, according to the formula

$\omega=\dfrac{1}{2\pi}\sqrt{\dfrac{g}{l}}$

You can see how varying the length will change the frequency.

Physically, mass does not affect frequency because mass comes into play both in the force due to gravity and the acceleration is gets. The reasoning is similar to how $g$ is same regardless of mass. In the mathematical treatment, the mass terms occurs in both sides of the equation and gets cancelled.

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