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Sine Acceleration Calculator

Formula

To calculate the Sine Acceleration:

$a = -2\pi f^2 D \sin(2\pi f t)$

Where:

$a$ is the Sine Acceleration (m/s²)
$f$ is the frequency (Hz)
$D$ is the displacement (m)
$t$ is the time (s)

What is Sine Acceleration?

Sine acceleration refers to the acceleration experienced by an object in harmonic motion, characterized by a sinusoidal displacement over time. It is typically measured in meters per second squared (m/s²), reflecting how quickly the velocity of the object changes in response to the sinusoidal displacement.

Example Calculation 1

Let's assume the following values:

Frequency ( $f$ ) = 5 Hz
Displacement ( $D$ ) = 0.1 m
Time ( $t$ ) = 2 s

Using the formula:

$a = -2 \times \pi \times 5^2 \times 0.1 \times \sin(2 \times \pi \times 5 \times 2)$

The sine acceleration is -49.47 m/s².

Example Calculation 2

Let's assume the following values:

Frequency ( $f$ ) = 10 Hz
Displacement ( $D$ ) = 0.05 m
Time ( $t$ ) = 1 s

Using the formula:

$a = -2 \times \pi \times 10^2 \times 0.05 \times \sin(2 \times \pi \times 10 \times 1)$

The sine acceleration is -197.39 m/s².