Novel Approximations to the Damped Parametric Driven Pendulum Oscillators

The damped parametric driven nonlinear pendulum equation/oscillator (NPE), also known as the disturbed NPE, is examined, along with some associated oscillators for arbitrary angles vertical pivot. For analyzing and solving current equation, we reduce this equation to Duffing (DDE) variable coefficients. After that, DDE coefficients divided into two cases. In first case, analytical approximations undisturbed NPE are obtained. approximation determined using ansatz method while second one derived He’s frequency formulation. i.e., three in terms of trigonometric Jacobi elliptic functions discussed method. semianalytical solutions mentioned cases graphically compared 4th-order Runge–Kutta (RK4) approximations. addition, maximum error all estimated RK4 approximation. proposed approaches well obtained may greatly help understanding mysteries various phenomena that arise different scientific fields such fluid mechanics, plasma physics, engineering, electronic chips.