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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
 one year ago
 one year ago
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
 one year ago
 one year ago

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akash123Best ResponseYou've already chosen the best response.1
write down the equation of motion for pendulum
 one year ago

akash123Best ResponseYou've already chosen the best response.1
dw:1349777134567:dw
 one year ago

apple_piBest ResponseYou've already chosen the best response.0
why is the mg force not straight down?
 one year ago

akash123Best ResponseYou've already chosen the best response.1
sorry...mg is straight down only
 one year ago

akash123Best ResponseYou've already chosen the best response.1
does it help u in finding the time period?
 one year ago

apple_piBest ResponseYou've already chosen the best response.0
I want to know how the formula is derived...
 one year ago

akash123Best 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
 one year ago

akash123Best ResponseYou've already chosen the best response.1
net force along tangent is mg sin (theta)
 one year ago

akash123Best ResponseYou've already chosen the best response.1
now v_tangential= r ( angular vel)
 one year ago

akash123Best ResponseYou've already chosen the best response.1
differentiate it a_tangential= r(angular acc)
 one year ago

akash123Best ResponseYou've already chosen the best response.1
r is the length of pendulum in this case
 one year ago

akash123Best ResponseYou've already chosen the best response.1
now substitute a_tangential into m( a_t) = mg sin(theta)
 one year ago

apple_piBest ResponseYou've already chosen the best response.0
m(r*angular_acc) = m(sin(theta))
 one year ago

akash123Best ResponseYou've already chosen the best response.1
m ( l(angular acc))= mg sin(theta)....l=r= length of pendulum
 one year ago

akash123Best ResponseYou've already chosen the best response.1
now l(angular acc))= g sin(theta)
 one year ago

apple_piBest ResponseYou've already chosen the best response.0
where did the l come from?
 one year ago

akash123Best 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
 one year ago

apple_piBest ResponseYou've already chosen the best response.0
oh right... l = r. I forgot about that
 one year ago

akash123Best ResponseYou've already chosen the best response.1
now acceleration = g/l sin(theta)
 one year ago

akash123Best ResponseYou've already chosen the best response.1
equation of SHM is a=  w^2 x then time period T= 2 pi/w
 one year ago

apple_piBest ResponseYou've already chosen the best response.0
I havent learnt SHM yet. whats w?
 one year ago

akash123Best 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
 one year ago

akash123Best ResponseYou've already chosen the best response.1
u know wave... omega= 2 pi (nu)
 one year ago

akash123Best 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.
 one year ago

apple_piBest ResponseYou've already chosen the best response.0
ok. I know the basics of it
 one year ago

akash123Best ResponseYou've already chosen the best response.1
ok.. so acceleration = g/l (theta)
 one year ago

akash123Best ResponseYou've already chosen the best response.1
now compare this with a=  w^2 x where x is the displacement from fixed point
 one year ago

apple_piBest ResponseYou've already chosen the best response.0
so for small angle x = theta
 one year ago

akash123Best ResponseYou've already chosen the best response.1
so acceleration and displacement are in opposite direction
 one year ago

akash123Best ResponseYou've already chosen the best response.1
here theta is x.... for small angle sin(theta)= theta
 one year ago

akash123Best ResponseYou've already chosen the best response.1
so in the case of pendulum angular displacement and angular acceleration are in opposite direction
 one year ago

akash123Best 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!
 one year ago

akash123Best ResponseYou've already chosen the best response.1
so for small x sin x =x
 one year ago

akash123Best ResponseYou've already chosen the best response.1
neglect higher order terms
 one year ago

akash123Best ResponseYou've already chosen the best response.1
so we have acceleration = g/l (theta)
 one year ago

apple_piBest ResponseYou've already chosen the best response.0
I forgot what w is equal to
 one year ago

akash123Best ResponseYou've already chosen the best response.1
w= angular frequency= 2 pi( frequency)
 one year ago

akash123Best ResponseYou've already chosen the best response.1
T= (2 pi)/ (2 pi( frequency))
 one year ago

apple_piBest ResponseYou've already chosen the best response.0
so where does the √ come in?
 one year ago

akash123Best ResponseYou've already chosen the best response.1
w^2= g/l so what will be w?
 one year ago

akash123Best ResponseYou've already chosen the best response.1
so u got the time period.
 one year ago

apple_piBest ResponseYou've already chosen the best response.0
I see one problem though... this will only be accurate with small angles right?
 one year ago
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