Question

What type of graph do you expect between (i) L and T and (ii) L and T^2 ?

Answer 1

The type of graph expected between is

(i) Straight line passing through origin

(ii) Parabolic graph

Answer 2

The type of graph that we expect between

(i) L and T  - a parabolic curve

(ii) L and T^2 - a straight line

The simple pendulum exhibits simple harmonic motion.

The time period (T) of a simple pendulum for oscillations of small amplitude, is given by the relation ,

T = 2π√(L/g)

⇒ T = k √L

⇒ T² = (k) L  ...........(1)

The standard equation of parabola is given by,

y² = (4a) x ...........(2)

comparing  (1) and (2), we get a parabolic curve for L and T.........(i)

Squaring the equation of time period, we get

T² = 4π²(L/g)

⇒ T² = (4π²/g) L + 0 ..........(3)

with slope 4π².

The standard equation of a straight line is given by,

y = mx + c ..........(4)

comparing  (3) and (4), we get a straight line for L and T².........(ii)