Stabilization of Driven Pendulum with Periodic Linear Forces

Table 2

Stability comparison of periodic piecewise linear forces with harmonic force under vertical fast oscillation.

Force type	Position	Stability condition	Position	Stability condition
Sin	0	Always	𝜋	𝜔^2>2𝑔𝑙
Triangular	0	Always	𝜋	𝜔^2>3.0396𝑔𝑙
Linear (sine)	0	Always	𝜋	𝜔^2>2.172𝑔𝑙
Trapezium	0	Always	𝜋	𝜔^2>1.4736𝑔𝑙
Quadratic	0	Always	𝜋	𝜔^2>1.2967𝑔𝑙
Rectangular	0	Always	𝜋	𝜔^2>1.2159𝑔𝑙