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.