Enter the frequency, displacement, and time into the calculator to determine the Sine Acceleration. 

Sine Acceleration Formula

The following equation is used to calculate the Sine Acceleration.

a = -2*pi*f^2*D*sin(2*pi*f*t)
  • Where a is the Sine Acceleration (m/s^2)
  • f is the frequency (hz)
  • D is the displacement (m)
  • t is the time (s)

What are the units for Sine Acceleration?

The most common units for Sine Acceleration are m/s^2.

How to Calculate Sine Acceleration?

Example Problem:

The following example problem outlines the steps and information needed to calculate the Sine Acceleration.

First, determine the frequency. In this example, the frequency is determined to be 500 (hz).

Next, determine the displacement. For this problem, the displacement is measured to be 3 (m).

Next, determine the time. In this case, the time is found to be 30 (s).

Finally, calculate the Sine Acceleration using the formula above: 

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

Inserting the values from above and solving the equation with the imputed values gives: 

a = -2*3.14159*500^2*3*sin(2*3.1415*500*30) =1668802.81 (m/s^2)


What is Sine Acceleration and how is it used in physics?
Sine Acceleration is a measure of how an object’s velocity changes over time in a sinusoidal pattern, typically as a result of oscillatory motions or wave phenomena. It is crucial in the study of vibrations, waves, and any system where motion repeats in a cyclical manner. This concept helps in understanding the dynamic behavior of systems under sinusoidal forces.

Why is the formula for Sine Acceleration important in engineering and physics?
The formula for Sine Acceleration is essential because it provides a mathematical way to predict how objects will move under sinusoidal forces, which is common in many engineering applications such as mechanical vibrations, acoustics, and electromagnetic waves. It allows engineers and physicists to design systems that can withstand or utilize these forces effectively, ensuring safety and efficiency in various technologies.

Can Sine Acceleration be negative, and what does that indicate?
Yes, Sine Acceleration can be negative. In the context of the formula, a negative acceleration indicates that the object is decelerating or accelerating in the opposite direction of its initial motion. This is a natural part of sinusoidal motion, where the acceleration direction changes as the object moves through its cycle, reflecting the oscillatory nature of the motion.