write the equation of motion of a simple pendulum and use it to obtain the condition under which its motion is simple harmonic in nature obtain an expression for its time period under this condition
Answers
Answer:
Explanation:
Ideal simple pendulum is defined as a heavy point mass suspended from a rigid support by a weightless and inextensible string and set oscillating under gravity through a small angle in a vertical plane.
Let a simple pendulum of length L suspended from a rigid support O. Let it is displaced by a small angle θ in a vertical plane and released. Resolving mg into horizontal and vertical components at point B as mgcosθ and mgsinθ respectively.
We see that restoring force
F=−mgsinθ
If 'θ ' is small then
sinθ=θ=
L
x
F=−mgθ
=−mg
L
xWe see that F∝(−x)
Since F is directly proportional to negative of displacement so motion of a simple pendulum is in linear S.H.M.
So acceleration =
m
F
=
L
−acceleration per unit displacement
∣
∣
∣
∣
x
a
∣
∣
∣
∣
=
L
g
T=
accelerationperunitdisplacement
2π
=
L
g
2π
T=2π
g
L
