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The Kinematics of Linear SHM calculator will calculate:

- Angle to the vertical direction of a simple pendulum at any instant
- Angular velocity of a simple pendulum's bob at any instant
- Angular acceleration of a simple pendulum's bob at any instant

The angle to the vertical direction of a simple pendulum at any instant is rad |

The angular velocity of a simple pendulum's bob at any instant is rad/s |

The angular acceleration of a simple pendulum's bob at any instant is rad/s^{2} |

Thread's angle to the vertical direction calculation |
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θ(t) = θ_{0} × cos( × t)2π/Tθ(t) = × cos( × 2 × /)θ(t) = × cos( × /)θ(t) = × cos( × )θ(t) = × cos()θ(t) = × θ(t) = |

Angular velocity of the pendulum calculation |

ω(t) = -θ_{0} × × sin(2π/T × t)2π/Tω(t) = - × × sin(2 × / × 2 × /)ω(t) = - × × sin(/ × /)ω(t) = - × × sin( × )ω(t) = - × × sin()ω(t) = - × × ω(t) = |

Angular acceleration of the pendulum's bob calculation |

α(t) = -θ_{0} × ()2π/T^{2} × cos( × t)2π/Tα(t) = - × ()2 × /^{2} × cos( × 2 × /)α(t) = - × ()/^{2} × cos( × /)α(t) = - × ()^{2} × cos( × )α(t) = - × × cos()α(t) = - × × α(t) = |

Kinematics of Linear SHM Calculator Input Values |

Angular amplitude of oscillation (θ_{0}) rad |

Period of oscillation (T) s |

Archimedes' constant (π) |

Time (t) s |

Please note that the formula for each calculation along with detailed calculations are available below. As you enter the specific factors of each kinematics of linear shm calculation, the Kinematics of Linear SHM Calculator will automatically calculate the results and update the Physics formula elements with each element of the kinematics of linear shm calculation. You can then email or print this kinematics of linear shm calculation as required for later use.

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θ(t) = θ_{0} × cos (*2π**/**T* × t)

ω(t) = -θ_{0} × *2π**/**T* × sin (*2π**/**T* × t)

α(t) = -θ_{0} × (*2π**/**T*)^{2} × cos (*2π**/**T* × t)

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