This equation computes the linear acceleration in the x-direction of a simple harmonic oscillator.

When the restoring force is directly proportional to the displacement from equilibrium, the oscillation is called Simple Harmonic Motion (SHM).

The constant, k, which characterizes the restoring force of an ideal spring is expressed in units of Newtons/ meters (N/m) or alternatively, `(kg)/s^2`.

Inputs

• m - mass of the oscillating object
• x - displacement distance of the oscillating object

Derivation

Since the restoring of force of a simple harmonic oscillator is given by `F_x = k*x` ^{[ 1 ]} , then also `F_x = m * a_x`, and so

     `a_x = F_x / m = (-k*x) / m`
 

Sources

Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 421, eq 13.4

1. ^ Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 421, eq 13.3