Kinematics of Linear SHM Calculator

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

Kinematics of Linear SHM Calculator
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Calculator Precision (Decimal Places)
Angular amplitude of oscillation (θ₀) rad
Period of oscillation (T) s
Archimedes' constant (π)
Time (t) s

Kinematics of Linear SHM Calculator Results (detailed calculations and formula below)
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) =
Angular velocity of the pendulum calculation
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) =
Angular acceleration of the pendulum's bob calculation
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) =
Kinematics of Linear SHM Calculator Input Values
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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Discover Physics with free Physics Revision Notes and Physics Calculator: Kinematics of Linear SHM. This image shows the properties and kinematics of linear shm formula for the Kinematics of Linear SHM. This calculator will calculate the angle to the vertical direction of a simple pendulum at any instant, the angular velocity of a simple pendulum's bob at any instant and the angular acceleration of a simple pendulum's bob at any instant

Thread's angle to the vertical direction Formula and Calculation

θ(t) = θ₀ × cos (2π/T × t)

Angular velocity of the pendulum Formula and Calculation

ω(t) = -θ₀ × 2π/T × sin (2π/T × t)

Angular acceleration of the pendulum's bob Formula and Calculation

α(t) = -θ₀ × (2π/T)² × cos (2π/T × t)

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