Question

If the period of oscillation of a simple pendulum depends on length of the

pendulum, mass of the bob and acceleration due to gravity, derive the equation

for period of oscillation of simple pendulum using dimensional analysis​

Answer 1

Answer:

let w be omega which is angular velocity,

circumference of a circle is 2πr which is distance,

v is the velocity

and v=(perpendicular distance)*(angular velocity)

we know that

time=distance/speed

t=2πr/rw

t=2π/w

but from angular acceleration formula w²=a/y then w= √(a/y). where a is angular acceleration and y is angular displacement.

thus, t=2π/√(a/y)

t=(2π)*√(y/a)

where a can be referred as acceleration due to gravity in some cases.