# Kinematics of Linear SHM Calculator

The Kinematics of Linear SHM calculator will calculate:

1. Angle to the vertical direction of a simple pendulum at any instant
2. Angular velocity of a simple pendulum's bob at any instant
3. Angular acceleration of a simple pendulum's bob at any instant
 🖹 Normal View🗖 Full Page View Calculator Precision (Decimal Places)0123456789101112131415 Angular amplitude of oscillation (θ0) rad Period of oscillation (T) s Archimedes' constant (π) Time (t) s
Thread's angle to the vertical direction calculation 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/s2 θ(t) = θ0 × cos(2π/T × t)θ(t) = × cos(2 × / × )θ(t) = × cos(/ × )θ(t) = × cos( × )θ(t) = × cos()θ(t) = × θ(t) = ω(t) = -θ0 × 2π/T × sin(2π/T × t)ω(t) = - × 2 × / × sin(2 × / × )ω(t) = - × / × sin(/ × )ω(t) = - × × sin( × )ω(t) = - × × sin()ω(t) = - × × ω(t) = α(t) = -θ0 × (2π/T)2 × cos(2π/T × t)α(t) = - × (2 × /)2 × cos(2 × / × )α(t) = - × (/)2 × cos(/ × )α(t) = - × ()2 × cos( × )α(t) = - × × cos()α(t) = - × × α(t) = Angular amplitude of oscillation (θ0) 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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## Related Physics Chapters with Tutorials

Section 3: Kinematics

Section 10: Oscilations

## Thread's angle to the vertical direction Formula and Calculation

θ(t) = θ0 × cos (/T × t)

## Angular velocity of the pendulum Formula and Calculation

ω(t) = -θ0 × /T × sin (/T × t)

## Angular acceleration of the pendulum's bob Formula and Calculation

α(t) = -θ0 × (/T)2 × cos (/T × t)

## Oscilations Physics Tutorials associated with the Uniform Motion Calculator

The following Physics tutorials are provided within the Oscilations section of our Free Physics Tutorials. Each Oscilations tutorial includes detailed Oscilations formula and example of how to calculate and resolve specific Oscilations questions and problems. At the end of each Oscilations tutorial you will find Oscilations revision questions with a hidden answer that reveals when clicked. This allows you to learn about Oscilations and test your knowledge of Physics by answering the test questions on Oscilations.

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