Time period of 2 disks connected by a spring

In summary: Thanks and good luck!Then I'll close this thread for now. Let me know if you want it back open (send me a message by clicking on my avatar and "Start a Conversation"). Thanks and good luck!
  • #1
Vivek33010
3
2
Homework Statement
2 identical disks (1 & 2) each of mass M and radius R are lying on a flat surface. They are free to rotate about their axis. They are connected by a spring of spring constant 'K'.
Find time period of small oscillations such that :-
Case A: spring 1 and 2 always rotate in same sense.
Case B: spring 1 and 2 always rotate in opposite sense.
Relevant Equations
torque(τ) = (radius vector)×(force vector)
torque(τ) = (moment of inertia I)(angular acceleration α)
Equation of angular SHM, α = -(ω^(2))(θ)
My attempt at solving case B

I've attached my attempt at case B above. What problem I'm facing is that after writing equation of angular SHM, I'm getting angular acceleration proportional to cube of angular displacement, which doesn't reduce to SHM. So how to find time period for this oscillations, or how to reduce it to SHM?Proper diagram with question
 
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  • #2
Vivek33010 said:
Homework Statement:: 2 identical disks (1 & 2) each of mass M and radius R are lying on a flat surface. They are free to rotate about their axis. They are connected by a spring of spring constant 'K'.
Find time period of small oscillations such that :-
Case A: spring 1 and 2 always rotate in same sense.
Case B: spring 1 and 2 always rotate in opposite sense.
Relevant Equations:: torque(τ) = (radius vector)×(force vector)
torque(τ) = (moment of inertia I)(angular acceleration α)
Equation of angular SHM, α = -(ω^(2))(θ)

My attempt at solving case B

I've attached my attempt at case B above. What problem I'm facing is that after writing equation of angular SHM, I'm getting angular acceleration proportional to cube of angular displacement, which doesn't reduce to SHM. So how to find time period for this oscillations, or how to reduce it to SHM?Proper diagram with question
Welcome to PF. :smile:

Unfortunately, the image is unreadable. Maybe instead, check out the "LaTeX Guide" link below, and type your work into the Edit window? That makes it a lot easier to read and reply to. Thanks. :smile:

1619022424360.png
 
  • #3
berkeman said:
Welcome to PF. :smile:

Unfortunately, the image is unreadable. Maybe instead, check out the "LaTeX Guide" link below, and type your work into the Edit window? That makes it a lot easier to read and reply to. Thanks. :smile:

View attachment 281834
I write a new question or just edit this one?
 
  • #4
You can just reply below with the update to this problem. Or do you mean what you should do if you have a new/different question? In that case please start a new thread. Basically it is one thread per question/problem.
 
  • #5
berkeman said:
You can just reply below with the update to this problem. Or do you mean what you should do if you have a new/different question? In that case please start a new thread. Basically it is one thread per question/problem.
I'll make a new thread, with the same question, but with better representation. I'll see if I can use latex because I don't know what it is. New thread coming right up
 
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  • #6
Then I'll close this thread for now. Let me know if you want it back open (send me a message by clicking on my avatar and "Start a Conversation").
 

Related to Time period of 2 disks connected by a spring

1. What is the equation for the time period of 2 disks connected by a spring?

The equation for the time period of 2 disks connected by a spring is T = 2π√(m/k), where T is the time period, m is the mass of the disks, and k is the spring constant.

2. How does the mass of the disks affect the time period?

The time period is directly proportional to the square root of the mass of the disks. This means that as the mass increases, the time period also increases.

3. How does the spring constant affect the time period?

The time period is inversely proportional to the square root of the spring constant. This means that as the spring constant increases, the time period decreases.

4. Does the amplitude of the motion affect the time period?

No, the amplitude of the motion does not affect the time period. The time period only depends on the mass of the disks and the spring constant.

5. Can the time period be calculated if the mass and spring constant are unknown?

No, the time period cannot be calculated without knowing the mass and spring constant. These two variables are necessary in the equation for the time period.

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