### Resumé

describing the oscillations of the damped nonlinear pendulum at large angles

is presented. The solution is expressed in terms of the Jacobi elliptic functions

by including a parameter-dependent elliptic modulus. The analytical solution

is compared with the numerical solution and the agreement is found to be

very good. In particular, it is found that the points of intersection with the

abscissa axis of the analytical and numerical solution curves generally differ

by less than 0.1%. An expression for the period of oscillation of the damped

nonlinear pendulum is presented, and it is shown that the period of oscillation

is dependent on time. It is established that, in general, the period is longer than

that of a linearized model, asymptotically approaching the period of oscillation

of a damped linear pendulum.

Originalsprog | Engelsk |
---|---|

Tidsskrift | European Journal of Physics |

Vol/bind | 35 |

Udgave nummer | 3 |

Antal sider | 13 |

ISSN | 0143-0807 |

DOI | |

Status | Udgivet - 2014 |

### Citer dette

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*European Journal of Physics*, bind 35, nr. 3. https://doi.org/10.1088/0143-0807/35/3/035014

**An analytical solution to the equation of motion for the damped nonlinear pendulum.** / Johannessen, Kim.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

TY - JOUR

T1 - An analytical solution to the equation of motion for the damped nonlinear pendulum

AU - Johannessen, Kim

PY - 2014

Y1 - 2014

N2 - An analytical approximation of the solution to the differential equationdescribing the oscillations of the damped nonlinear pendulum at large anglesis presented. The solution is expressed in terms of the Jacobi elliptic functionsby including a parameter-dependent elliptic modulus. The analytical solutionis compared with the numerical solution and the agreement is found to bevery good. In particular, it is found that the points of intersection with theabscissa axis of the analytical and numerical solution curves generally differby less than 0.1%. An expression for the period of oscillation of the dampednonlinear pendulum is presented, and it is shown that the period of oscillationis dependent on time. It is established that, in general, the period is longer thanthat of a linearized model, asymptotically approaching the period of oscillationof a damped linear pendulum.

AB - An analytical approximation of the solution to the differential equationdescribing the oscillations of the damped nonlinear pendulum at large anglesis presented. The solution is expressed in terms of the Jacobi elliptic functionsby including a parameter-dependent elliptic modulus. The analytical solutionis compared with the numerical solution and the agreement is found to bevery good. In particular, it is found that the points of intersection with theabscissa axis of the analytical and numerical solution curves generally differby less than 0.1%. An expression for the period of oscillation of the dampednonlinear pendulum is presented, and it is shown that the period of oscillationis dependent on time. It is established that, in general, the period is longer thanthat of a linearized model, asymptotically approaching the period of oscillationof a damped linear pendulum.

U2 - 10.1088/0143-0807/35/3/035014

DO - 10.1088/0143-0807/35/3/035014

M3 - Journal article

VL - 35

JO - European Journal of Physics

JF - European Journal of Physics

SN - 0143-0807

IS - 3

ER -