# Time period/frequency of pendulums with different mass and lengths

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.

• What do you understand by the pendulum effect? – Gert Nov 21 '16 at 1:48
• @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? – John M. Nov 21 '16 at 2:28
• Yes, the mass of the bob has no effect on frequency! Fact. en.wikipedia.org/wiki/Pendulum#Period_of_oscillation – Gert Nov 21 '16 at 2:36

The mass had no effect on the frequency/time period. However, if length is halved, frequency becomes $\sqrt{2}$ times, according to the formula
$\omega=\dfrac{1}{2\pi}\sqrt{\dfrac{g}{l}}$
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.