suppose there is a string,being divided into ratio 4:3 by point P.Larger part of the string has greater density than smaller one,and smaller part has greater cross section area than bigger 1....
what shud be the minimum frequency imparted to the string so that point P becomes node?

Question

SAGAR SINGH - IIT DELHI · Answer

Dear student,

The pendulum is modeled as a point mass at the end of a massless rod. We define the following variables:

θ = angle of pendulum (0=vertical)
R = length of rod
T = tension in rod
m = mass of pendulum
g = gravitational constant

We will derive the equation of motion for the pendulum using the rotational analog of Newton's second law for motion about a fixed axis, which is τ = I α where

τ = net torque
I = rotational inertia
α = θ''= angular acceleration

The rotational inertia about the pivot is I = m R². Torque can be calculated as the vector cross product of the position vector and the force. The magnitude of the torque due to gravity works out to be τ = −R m g sin θ. So we have −R m g sin θ = m R² α

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suppose there is a string,being divided into ratio 4:3 by point P.Larger part of the string has greater density than smaller one,and smaller part has greater cross section area than bigger 1.... what shud be the minimum frequency imparted to the string so that point P becomes node?