Questions - solving pendulum period of rotation

[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?

 

[Physics7]

please help me az fast as possible

 

[HallsofIvy]

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.

 

[Physics7]

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...

 

[haruspex]

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

Change in temperature, I would think. And l_m must be the linear coefficient of expansion.

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.

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.

 

[Physics7]

Change in temperature, I would think. And l_m 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.

could you please tell more about it? and explain it?

 

[haruspex]

could you please tell more about it? and explain it?

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.

 

[Physics7]

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

 

[haruspex]

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

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?

 

[Physics7]

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?

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

 

[haruspex]

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

 

[Physics7]

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 don't know how to do diffrential equation for it...

 

[haruspex]

I understand that complex pendulum period of rotation would be like this

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.