23u r still doing approximations ,
ur displacement is Lθ , not Lsinθ
so u unknowningly approximated sinθ≈θ
1.We know that the formula for time period for a simple pendulum is
2pi√(l/g).While deriving the formula we say that Theta is small so sin Theta is aproximately =theta.Thus the formula is valid for small oscillations.
Now another proof,
let us consider the SHM to be a linear SHM
Thus from figure,
x= l sin (theta)......1
Frestoring=mg sin(theta)
From 1,sin(theta)=x/l
Thus ,Frestoring=mgx/l=mw^2x, i.e w=√g/l
Threfore,T=2 pi √l/g.
Here, we did'nt use any aproxiimation like theta is small.So, the formula is valid for all values of theta (big or small !) or is it???
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5 Answers
1if theta will be big the restorig torque will nt be linear.so no shm only periodic..if theta is small it will be shm
23
11@querty
Here x=l sin(theta) and x is the displacement from mean position.
