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#1 2014-12-29 00:30:34
Spring Problem
Three identical point masses of mass m each are placed at the vertices of an equilateral triangle and joined through springs of equal length and spring constant k . The system is placed on a smooth table. If the masses are displaced a little towards the centroid of the triangle then time period of oscillation of the system is :
A)2π√(m/k)
B)2π√(m/2k)
C)2π/√(m/3k)
D)2π√(m/5k)
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#2 2014-12-29 21:40:01
- Bob
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Re: Spring Problem
hi Agnishom,
I did this as follows:
(1) Get an equation for the tension (compression) in one spring based on an extension 'e'.
(2) Consider the (outward) forces on a single mass, trying to restore the mass to its start position. Two springs will contribute and you'll need to resolve the tensions into a component perpendicular to the movement which you can ignore, and a component in the direction of the movement.
(3) Convert 'e' into a movement 'x' in the direction of the movement.
(4) Construct the equation of motion, with d2x/dt^2 and -x. Hence demonstrate simple harmonic motion and derive the period.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#3 2014-12-29 21:48:14
Re: Spring Problem
Two springs will contribute and you'll need to resolve the tensions into a component perpendicular to the movement which you can ignore, and a component in the direction of the movement.
I cannot get such a component.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#4 2014-12-30 04:34:54
- Bob
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Re: Spring Problem
Then I see
I am getting a sqrt(3)*kx N force outwards
elsewhere.
Here's a start:
Distinguish between 'e' along a side of the triangle, and 'x' in the direction the mass will move.
(1) T = ke.
(2) Component towards a vertex of one such force = Tcos(30). => a pair makes 2Tcos(30)
But convert the 'e' into an 'x', the movement in the direction of travel.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#5 2014-12-31 02:22:17
Re: Spring Problem
Which is the component which can be ignored and why can it be?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#6 2015-01-01 01:41:47
- Bob
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- Registered: 2010-06-20
- Posts: 10,643
Re: Spring Problem
The larger triangle shows the rest position. If mass A is moved inward to point D, the smaller triangle shows the masses and springs at this moment
e = AB
x = AD
The compressive force T can be split into two components, Tcos(30) towards A and Tsin(30) perpendicular to this direction.
The force on the other side is similar, so the effective force 'up' is 2Tcos(30). The two 'across' components oppose each other and so cancel out.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#7 2015-01-01 18:04:32
Re: Spring Problem
I am getting B as an answer
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#8 2015-01-02 02:30:46
- Bob
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- Registered: 2010-06-20
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Re: Spring Problem
Me too.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#9 2015-01-02 02:40:46
Re: Spring Problem
Why didn't adding the forces vectorwise work?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#10 2015-01-02 06:30:04
- Bob
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- Registered: 2010-06-20
- Posts: 10,643
Re: Spring Problem
You'll have to post what you tried.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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