Home | | Physics | | Physics | Laws of pendulum

Chapter: 11th 12th std standard Class Physics sciense Higher secondary school College Notes

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

Laws of pendulum

Laws of pendulum
From the expression for the time period of oscilations of a pendulum the following laws are enunciated. ( i) The law of length (ii)The law of acceleration (iii) The law of mass (iv)The law of amplitude

Laws of pendulum

From the expression for the time period of oscilations of a pendulum the following laws are enunciated.

         ( i) The law of length

The period of a simple pendulum varies directly as the square root of the length of the pendulum. (i.e) T α l

(ii)The law of acceleration

The period of a simple pendulum varies inversely as the square root of the acceleration due to gravity.

(i.e) T α 1 g

(iii) The law of mass

 The time period of a simple pendulum is independent of the mass and material of the bob.

(iv)The law of amplitude

The period of a simple pendulum is independent of the amplitude provided the amplitude is small.

 

Note : The length of a seconds pendulum is 0.99 m whose period is two seconds.

 

2 = 2π.rt(l/g)

l=  9.81x 4 / 4 π2=0.99 m

Oscillations of simple pendulum can also be regarded as a case of angular SHM.

Let θ be the angular displacement of the bob B at an instant of time. The bob makes rotation about the horizontal line which is perpendicular to the plane of motion as shown in Fig..


Restoring torque about O is τ = − mg l sin θ

τ = −m g l θ [ θ is sm all] ...(1)

 

Moment of inertia about the axis = m l 2 ...(2)

If the amplitude is small, motion of the bob is angular simple harmonic. Therefore angular acceleration of the system about the axis of rotation is

α = r/l = -mgl θ / ml2

α = - (g/l) θ   ?.(3)

We know that α = −ω 2 θ        ??.(4)

Comparing (3) and (4)

−ω 2θ = -(g/l) θ

angular frequency ω = rt(g/l)

Time period T = = 2π / ω = 2π .rt(l/g)

Frequency n = 1 / 2 π . rt(g/l)


Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail


Copyright © 2018-2020 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.