A simple pendulum in a stationary life has time period T. What would be the effect on the
time period when the lift i) Move Up with uniform velocity ii) Moves Down with uniform
velocity iii) Moves Up with uniform acceleration a iv) Moves Down with uniform
acceleration ‘a’ v) Begins To fall freely under gravity?

Time period of a simple pendulum in a stationary lift; T = 2π
L
→ (1)
g
Time period of a simple pendulum in a lift moving up with uniform acceleration is
Tup = 2π
L
→ (2)
g +a
Time period of a simple pendulum in a lift moving down with uniform acceleration is
Tdown = 2π
L
→ (3)
g −a
i) Moves up with uniform velocity, acceleration of lift at = 0
Then Top = 2π
L
= T [∵ (1)]
g
∴ No change in time period
ii) Moves down with uniform velocity a = 0
Then Tdown = 2π
L
= T [∵ (1)]
g
∴ No change in time period
Tup
(2)
⇒
=
(1)
T
g
⇒ Tup
g+a
∴ The lift moves up with uniform acceleration a, time period decreases
iv)
T
(3)
⇒ down =
(1)
T
g
⇒ Tdown > T
g −a
∴ The lift moves down with uniform acceleration a, time period increases
v) When the lift falls freely under gravity a = g
⇒ Tdown =
7.
L
=
g−g
L
= infinity