Time period of a simple pendulum depends on the length of a simple pendulum and acceleration due to gravity at a place obtain expression for time period by the method of dimensional analysis
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Explanation:
Mass of the bob = m
Acceleration due to gravity = g
Length of string = L
Let
⇒a=0 ⇒ Time period of oscillation is independent of mass of the bob
-2b=1
⇒b=-
b+c = 0
- + c =0
c=
Giving values to a,b and c in first equation
The real expression for Time period is
Therefore time period of oscillation depends only on gravity and length of the string.
Not on mass of the bob.
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taranjs123 Ambitious
The time period of oscillation of a simple pendulum depends on the following quantities. length of the pendulum, mass of the bob, and acceleration due to gravity. Derive the expression for time period using dimensional method.?
Report by Vyakundu5rbaby 22.04.2016
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Taranjs123 · Ambitious
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NikhilMTomy
NikhilMTomy Ambitious
Let Time period =T
Mass of the bob = m
Acceleration due to gravity = g
Length of string = L
Let T \alpha m ^{a}g ^{b}L ^{c}
[T] \alpha [m] ^{a}[g] ^{b}[L] ^{c}
M^{0}L^{0}T^{1}=M^{a}L^{b}T^{-2b}L^{c}
M^{0}L^{0}T^{1}=M^{a}L^{b+c}T^{-2b}
⇒a=0 ⇒ Time period of oscillation is independent of mass of the bob
-2b=1
⇒b=-\frac{1}{2}
b+c = 0
-\frac{1}{2} + c =0
c=\frac{1}{2}
Giving values to a,b and c in first equation
T \alpha m ^{0}g ^{- \frac{1}{2} }L ^{ \frac{1}{2} }
T \alpha \sqrt{ \frac{L}{g} }
The real expression for Time period is
T =2 \pi \sqrt{ \frac{L}{g} }
Therefore time period of oscillation depends only on gravity and length of the string.
Not on mass of the bob.
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The equation of time period of a pendulum is
Since 2π is a constant , the time period mainly depends on 2 parameters :
Length of pendulum
Gravitational acceleration at that place
Concept:
Length of pendulum means the distance of centre of mass of Bob from the separation distance. It doesn't just signify the real length of the string from which the Bob hangs.
Another thing is that :
Gravitational acceleration at any place depends on many factors like latitude , rotational motion of Earth , altitude of that place , etc. All these factor determine the time period of a pendulum.