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 2 years 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
 2 years 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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