# Pendulum Tilted at an Angle

1. Nov 14, 2015

### racwen

1. The problem statement, all variables and given/known data
What would the period be if the pendulum had been inclined to 90 degrees? What value of g does this correspond to?
theta=90degrees. Just as a side note, theta=0degrees when the arm is facing vertically downwards towards the ground.
g=9.8m/s^2
Effective length=0.275m. The value of length was found from the lab I carried out.
Mass attached to end of arm=0.176kg
2. Relevant equations
T=2pi x root(L/gcostheta) T is period.
ag=gcostheta. ag is acceleration due to gravity.
3. The attempt at a solution
T=2pi x root(0.275m/(9.8 x cos90))=undefined. Since ag=gcostheta=(9.8 x cos90)=undefined, there would be no acceleration acting on the pendulum, thus no force pushing the pendulum. As a result, the pendulum will not oscillate, and there would be no period. I'm not sure if this is correct, would a pendulum still oscillate when the arm is tilted at 90degrees, and how can period be undefined?

2. Nov 15, 2015

### haruspex

What if you think of it in terms of the angle tending to 90 degrees? What does the period tend to?

3. Nov 15, 2015

### J Hann

Remember that the equation T=2pi x root(L/g) T is period was derived
for small angles where sin theta approximately equals theta (usually less than 10 deg).
where did the equation T=2pi x root(L/gcostheta) come from?.

4. Nov 15, 2015

### haruspex

racwen is interpreting the problem as a pendulum with a tilted plane of oscillation. Given the question about the value of g, that does seem to be the right view.

5. Nov 15, 2015

### J Hann

OK, so theta in this sense is a constant in the derivation of the equation of a simple equation.

6. Nov 15, 2015

### racwen

The period depends on the length, and acceleration (including the angle). I'm not sure if that's what you mean?

7. Nov 15, 2015

### haruspex

No, I mean suppose it is tilted at some angle theta. You found the period for that. Now, instead of substituting theta equals 90 degrees, consider what happens to the period as theta tends towards 90 degrees. What value does the period tend to?

8. Nov 15, 2015

### racwen

As period approaches 90 degrees, the period increases. It goes past approximately 25.27s when I used theta=89.9degrees.

9. Nov 15, 2015

### haruspex

Yes, but what is the value in the limit as theta goes to 90?

10. Nov 15, 2015

### racwen

As theta approaches 90, the limit approaches infinity.

11. Nov 15, 2015

### haruspex

Right.

12. Nov 15, 2015

### racwen

So if the period does not exist at 90degrees, does that mean that the pendulum takes an infinite or unknown amount of time to complete one cycle?

13. Nov 15, 2015

### haruspex

The reason I took you through that approach using limits was to demonstrate that it is known.

14. Nov 15, 2015

### racwen

Ohh ok, thank you for your help.