# Simple pendulum in different situations

1. Dec 22, 2015

Say there is a pendulum which is suspended by a massless thread or rod or whatever, the bob is spherical and hollow. Now consider 2 cases 1) the pendulum is completely filled with water 2) the water inside freezes. will there be a difference in the time periods? If so, why?

2. Dec 22, 2015

### DuckAmuck

My first instinct is that not only will the period be different, but the behavior may even become chaotic when the water is liquid, like a double-pendulum.
The water sloshing inside the bob would add an extra degree of freedom, like a second pendulum.

Unless the bob is completely filled with water. I wouldn't expect a difference in that case.

3. Dec 22, 2015

### daniellionyang

If you disregard the friction of the water, isn't the water stationary? Also, if the water freezes, the bob has to expand right? since the period of a pendulum is 2pisqrt(l/g), there would be no difference. However, if the bob expands, that would slightly change l.

4. Dec 25, 2015

Well, I guess I should've stated some more conditions (being a student, I take them for granted) there is no friction due to water and neglect any changes in volume. Anyway, both of you say that there is Jo change, that must be it then.

5. Dec 26, 2015

### Ghost116

Equation needed: T=2π√(L/G). If the water is uniformly distributed and also fills up the entire sphere (to avoid sloshing which changes this whole problem), and we're ignorning friction, expansion, etc... Then no there should be no difference. The bob's center of mass remains in the center of the water (liquid/ice) as you can treat a sphere filled completely with water as a "solid" mass (ignoring the complicated stuff as this appears to).

6. Dec 26, 2015

### MidgetDwarf

Exactly what the previous poster mentioned. Because of your given constraints, and not a real world scenario, the Pendulum is mass independent. Therefore, I could fill it up with hot sauce, and the answer would be the same.

7. Dec 26, 2015

### just dani ok

I think you need to clarify this. Pendulum is not mass independent.

8. Dec 26, 2015

### MidgetDwarf

the period of the pendulum is mass independent.

9. Dec 26, 2015

### just dani ok

sorry, my mistake.