Dimensional analysis of simple pendulm

In summary, using dimensional analysis, the dependence of the period T of a simple pendulum on its mass, weight, length, and arc-length of swing is determined to be T = cst * m^a * l^b * g^c * s^d. However, the inclusion of the arc-length in the equation is incorrect, as it should not be considered in the calculation. The final equation for T is T = 2π(l/g)^1/2.
  • #1
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Homework Statement



Use dimensional analysis to determine the dependence of the period T of
a simple pendulum on its mass m , weight w , length l and arc-length of
swing s.

Homework Equations


g= [L/T2]

The Attempt at a Solution



T =cst * malbgcsd

[T]=malbgcsd
=[M]a[L]b[g]c[L]d
okay I am making a mistake here aren't I? by including the arc-Length? i do not know why i should not include it? some one explain? I am a bit confused... after this I'll be able to go on.

then i will equate the exponents and solve it.

EDIT: Thanks in advance
 
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  • #2
a=0
b+c+d=0
-2c=1 => c=-1/2

b+d=1/2 ==> b=d=1/4

T=l1/4g-1/2s1/4

but T= 2π (l/g)1/2

what i did is is correct?
 
  • #3
could someone help me out here?
 

1. What is dimensional analysis of a simple pendulum?

Dimensional analysis of a simple pendulum is a mathematical method used to analyze the physical quantities involved in the motion of a simple pendulum. It involves breaking down these quantities into their fundamental units and using them to derive equations that describe the behavior of the pendulum.

2. What are the fundamental quantities involved in a simple pendulum?

The fundamental quantities involved in a simple pendulum are length (L), mass (M), and time (T). These quantities are used to derive equations for the period and frequency of the pendulum's motion.

3. How does the length of a pendulum affect its period?

The length of a pendulum has a direct effect on its period, with longer pendulums having longer periods. This relationship is described by the equation T=2π√(L/g), where T is the period, L is the length, and g is the acceleration due to gravity.

4. Can dimensional analysis be used to analyze other types of pendulums?

Yes, dimensional analysis can be used to analyze any type of pendulum, as long as the fundamental quantities involved are known. This method can be applied to simple pendulums, compound pendulums, and even non-uniform pendulums.

5. How accurate is dimensional analysis in predicting the behavior of a pendulum?

Dimensional analysis is a highly accurate method for predicting the behavior of a pendulum. However, it assumes that the pendulum is in an ideal environment with no external factors affecting its motion. In real-life situations, there may be some discrepancies between the predicted and actual behavior of a pendulum.

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