# Questions - solving pendulum period of rotation

1. Dec 5, 2012

### Physics7

Questions -- solving pendulum period of rotation

Physical pendulum has a period of rotation
that changes by Changing the temperature.
According to the above show that the frequency shift of the pendulum would be:

I have 2 questions,first solving the above question
and the second how Rotation period of the pendulum could be like this?

Last edited: Dec 5, 2012
2. Dec 5, 2012

### Physics7

Re: Questions

3. Dec 5, 2012

### HallsofIvy

Staff Emeritus
Re: Questions

Your first question is incomplete. How is $\Delta \theta$ defined?

As for your second question, it is also incomplete. What are "I" and "d"? I can guess that m and g are mass and the acceleration of gravity and possibly that "d" is the length of the pendulum but my guess would be that "I" is moment of inertia but that does not fit here.

4. Dec 5, 2012

### Physics7

Re: Questions

my problem is these too,this is the book practice and hasn't explained anything even the professor didnt understand and he asked me to search for it....

5. Dec 5, 2012

### haruspex

Re: Questions

Change in temperature, I would think. And lm must be the linear coefficient of expansion.
Yes, I as moment of inertia makes sense. If we assume that, and that d is the length of the pendulum from axis to centre of gravity, and we assume the pendulum expands uniformly, then I get the same answer as the book.

6. Dec 6, 2012

### Physics7

Re: Questions

7. Dec 6, 2012

### haruspex

Re: Questions

Do you know how to write down the differential equation for a simple pendulum and solve it? You will need a version of it that does not treat the pendulum as a point mass at the end of a massless rod.

8. Dec 6, 2012

### Physics7

Re: Questions

I understand what you mean but I do' know how to solve it

9. Dec 6, 2012

### haruspex

Re: Questions

So you can write down the ODE? If so, please post it.
Are you expected to be able to solve SHM ODEs, or perhaps just expected to recognise them and quote a solution?

10. Dec 6, 2012

### Physics7

Re: Questions

sorry what do you mean by ode shm and odes ?
Im not native really sorry that bother you and put you in trouble :shy:

Last edited: Dec 6, 2012
11. Dec 6, 2012

### haruspex

Re: Questions -- solving pendulum period of rotation

Apologies. ODE = ordinary differential equation; SHM = simple harmonic motion.

12. Dec 7, 2012

### Physics7

Re: Questions -- solving pendulum period of rotation

I know the diffrential equation but not for pendulum.
and shm if you mean its okay,
I searched and I understand that complex pendulum period of rotation would be like this but dont know how to do diffrential equation for it...

13. Dec 7, 2012

### haruspex

Re: Questions -- solving pendulum period of rotation

OK, that should be enough for the question about change in temperature.
What you need to work out is how a small increase in length (resulting from a change in temperature) will affect I and d, and hence how it will affect the period. Do you understand how to use differentiation for that?
In the OP, you also said you wanted to know how the complex pendulum formula could be like that. To answer that, I need to walk you through the derivation and solution of the differential equation. OTOH, I get the impression you're not required to be able to do that yet. Please say how you'd like to proceed on that.