Mechanics Problem: Time Period of Simple Pendulum with Uniform Rod and Mass m

  • Thread starter neelakash
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In summary, the problem is about finding the new time period for small oscillations in a simple pendulum where the string has been replaced by a uniform rod of length L and mass M. The mass of the bob, m, is also given. The main challenge is to correctly account for the change in the system's center of gravity and moment of inertia due to the replacement of the string with a rod. The solution will involve deriving a new relation between the moment of inertia and the period for a physical pendulum.
  • #1
neelakash
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Homework Statement



In a simple pendulum the string supporting the bob is replaced by a uniform rod of length L and mass M.Find the nw time period for small oscillations.Mass of the bob m.

Any help how to do it correctly?

Homework Equations


The Attempt at a Solution



Any help how to do it correctly?
 
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  • #2
i guess the mass of string was neglected
and now since the rod has mass M, the CG of the system has changed
 
  • #3
Basically, this is a physical pendulum now. Sure, the centre of mass has changed. So has the moment of inertia. If I remember right, the moment of inertia of a physical pendulum determines its period, but you'll have to derive the exact relation.
 

FAQ: Mechanics Problem: Time Period of Simple Pendulum with Uniform Rod and Mass m

What is a simple pendulum?

A simple pendulum is a weight suspended from a fixed point that is allowed to swing freely back and forth under the influence of gravity. It consists of a small mass attached to a long, thin rod or string.

How is the time period of a simple pendulum calculated?

The time period of a simple pendulum is calculated using the equation T = 2π√(L/g), where T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity (usually taken as 9.8 m/s²).

How does the mass of the pendulum affect its time period?

The mass of the pendulum does not affect its time period. The time period is only dependent on the length of the pendulum and the acceleration due to gravity.

What is the effect of changing the length of the pendulum on its time period?

Changing the length of the pendulum will affect its time period. A longer pendulum will have a longer time period, while a shorter pendulum will have a shorter time period.

Can the time period of a simple pendulum be affected by external factors?

Yes, the time period of a simple pendulum can be affected by external factors such as air resistance, friction, and temperature. These factors can cause the pendulum to slow down or speed up, resulting in a slightly different time period than the calculated value.

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