Pendulum with its pivot accelerating upward

[AlonsoMcLaren]

A pendulum of length, b, and bob with mass, m, is attached to a massless support moving vertically upward with constant acceleration a. Find the equation of motion.

This problem is easy with the help of Lagrangian dynamics: bθ''+(g+a)θ=0

But how to solve this problem using Newton's formulation? I really have no idea... Apparently only the tension of the string and gravity are acting on the bob. But the tension of string seems very complicated...

 

[OldEngr63]

Start by writing the position of the pendulum bob in terms of the support position, ys, the pendulum length, and the angle of the pendulum. Then differentiate to find the acceleration of the bob. From there on it is fairly straight forward F = ma, with a support motion term included.

 

[rcgldr]

But how to solve this problem using Newton's formulation?

Just combine a+g and treat that sum as the effective amount of gravity for the pendulum.

 

[OldEngr63]

Draw the FBD, show the vectors, and then it will make more sense. Just talking about it does not help very much. You need to actually work with the math to see what is going on.