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?

Dear student,

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