Question

When a simple pendulum executes small amplitude oscillations in a medium (like air), its amplitude decreases, quite slowly

(1) with time (in a linear way) but its time period remains completely independent of its amplitude.

(2) with time (in a non–linear way) but it time period remains completely independent of its amplitude.

(3) with time (in a non–linear way) and its time period shows a slight increase compared to its time period in free space.

(4) With time (in a linear way) and its time period shows a slight decrease compared to its time period in free space.

Answer 1

(3) with time (in a non–linear way) and its time period shows a slight increase compared to its time period in free space.

The oscillations, of a pendulum bob, in a medium (like air) are damped oscillations. For such damped oscillations, the amplitude decreases exponentially with time, i.e., its decrease is a non–linear one. The time period, for such damped oscillations, is (slightly) more than its the time period in free space.