Difference between time period of a simple pendulum and a simple harmonic oscillator

  • Thread starter Anoushka
  • Start date
  • #1
Anoushka
2
0
can someone please tell me why is the time period of a simple pendulum independent of the mass m of the bob while the time period of a simple harmonic oscillator is T=2∏√m/k!
pleaseeeee help .

Thankyou sooo much :)
 

Answers and Replies

  • #2
collinsmark
Homework Helper
Gold Member
3,212
2,032


Hello Anoushka,

Welcome to Physics Forums!

can someone please tell me why is the time period of a simple pendulum independent of the mass m of the bob while the time period of a simple harmonic oscillator is T=2∏√m/k!
pleaseeeee help .

Thankyou sooo much :)
I can't give you the answer, but I will give you a couple things to consider.

//=============
// Consideration 1
//=============

It has been said that Galileo Galilei performed an experiment in which he simultaneously dropped two dense objects with unequal masses from the Leaning Tower of Pisa. Contrary to to the popular predictions of many other people, the objects hit the ground at the same time (even though one was significantly heavier than the other).

Jump forward a century or so and consider Isaac Newton's second law of motion.

[tex] \vec F = m \vec a [/tex]
Even if the mass [itex] m [/itex] is a variable in this equation, what it is that remains constant when considering objects falling due to gravity? Does [itex] \vec F [/itex] remain constant or does [itex] \vec a [/itex]?

Now it might help to repeat the same consideration, except instead of objects in perfect free fall, apply the considerations to various sized masses on a frictionless incline.

Can you see the relationship between that and an approximation to a pendulum? (Hint: assume small angles)

//=============
// Consideration 2
//=============

Now consider various sized masses attached to a particular, ideal spring. Suppose the spring also has particular compression x0 at some point in time.

Don't forget Newton's second law,
[tex] \vec F = m \vec a [/tex]
In this situation with a particular spring at a particular displacement, what is it that stays constant even if the mass changes? Does [itex] \vec F [/itex] remain constant or does [itex] \vec a [/itex]? :wink:
 
Last edited:
  • #3
marty1
81
0


A pendulum is an example of a simple harmonic ocillator.

Think about this too:

When you increase the mass of the pendulum the intertia of the pendulum increases the same as the force of gravity on the pendulum. The extra force of gravity is canceled exactly by the increase in inertia. Hence the resulting acceleration is constant but for a larger mass it take more force to achieve. Exactly the extra force provided by the addition mass.
 
  • #4
Anoushka
2
0


A pendulum is an example of a simple harmonic ocillator.

Think about this too:

When you increase the mass of the pendulum the intertia of the pendulum increases the same as the force of gravity on the pendulum. The extra force of gravity is canceled exactly by the increase in inertia. Hence the resulting acceleration is constant but for a larger mass it take more force to achieve. Exactly the extra force provided by the addition mass.

Marty1 and Collinsmark thanks a lot you guys , that was really helpful! :D
 

Suggested for: Difference between time period of a simple pendulum and a simple harmonic oscillator

Replies
20
Views
478
  • Last Post
Replies
6
Views
573
  • Last Post
Replies
14
Views
417
Replies
6
Views
703
Replies
7
Views
867
  • Last Post
Replies
11
Views
278
Replies
6
Views
311
Replies
6
Views
55
Replies
1
Views
431
Top