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apple_pi
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Where does the equation for simple pendulum motion come from? \[T=2\pi \sqrt{\frac{ l }{ g }}\] where T is period, l is string length, g is acc. due to gravity
 2 years ago
 2 years ago
apple_pi Group Title
Where does the equation for simple pendulum motion come from? \[T=2\pi \sqrt{\frac{ l }{ g }}\] where T is period, l is string length, g is acc. due to gravity
 2 years ago
 2 years ago

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akash123 Group TitleBest ResponseYou've already chosen the best response.1
write down the equation of motion for pendulum
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
dw:1349777134567:dw
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
why is the mg force not straight down?
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
sorry...mg is straight down only
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
does it help u in finding the time period?
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
I want to know how the formula is derived...
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
I know write down the equation of motion along the tangent... m( a_t) = mg sin(theta) a_ttangential acc
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
it's fine?
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
net force along tangent is mg sin (theta)
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
now v_tangential= r ( angular vel)
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
differentiate it a_tangential= r(angular acc)
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
r is the length of pendulum in this case
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
now substitute a_tangential into m( a_t) = mg sin(theta)
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
m(r*angular_acc) = m(sin(theta))
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
m ( l(angular acc))= mg sin(theta)....l=r= length of pendulum
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
now l(angular acc))= g sin(theta)
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
where did the l come from?
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
l=r=length of pendulum...pendulum is like bob is moving in a circle pivoted at centre
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
oh right... l = r. I forgot about that
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
now acceleration = g/l sin(theta)
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
equation of SHM is a=  w^2 x then time period T= 2 pi/w
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
I havent learnt SHM yet. whats w?
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
w(omega)angular frequency acceleration = g/l sin(theta) for small theta acceleration = g/l (theta) sin(theta)= theta
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
u know wave... omega= 2 pi (nu)
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
so we say SHM is a periodic motion in which acceleration is directed towards a fixed point which is called equilibrium point.
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
ok. I know the basics of it
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
ok.. so acceleration = g/l (theta)
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
for small theta
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
now compare this with a=  w^2 x where x is the displacement from fixed point
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
so for small angle x = theta
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
so acceleration and displacement are in opposite direction
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
yes seems logical
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
here theta is x.... for small angle sin(theta)= theta
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
so in the case of pendulum angular displacement and angular acceleration are in opposite direction
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
write six in the form a power series sin x= x  x^3/3! + x^5/5!
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
so for small x sin x =x
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
neglect higher order terms
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
so we have acceleration = g/l (theta)
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
so u have w^2= g/l
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
so T= 2 pi/w
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
I forgot what w is equal to
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
w= angular frequency= 2 pi( frequency)
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
so T = 2pi/2pi?
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
T= (2 pi)/ (2 pi( frequency))
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
so T= 1/ (frequency)
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
so where does the √ come in?
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
w^2= g/l so what will be w?
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
2π T= √(g/l)
 2 years ago

akash123 Group TitleBest ResponseYou've already chosen the best response.1
so u got the time period.
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
I see one problem though... this will only be accurate with small angles right?
 2 years ago
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