What are the characteristics of the simple harmonic motion on a spring?
1 Answer
The acceleration is proportional to the displacement (x) of the mass and it acts toward the equilibrium position.
The defining equation for any type of SHM is:
where
The negative indicates that the acceleration always acts toward the equilibrium.
In the plane of the oscillation for a horizontal mass–spring system the only (significant) force is the tension in the spring.
From Hooke’s Law:
Also the mass is not changing so we can apply the simplified form of Newton’s second law of motion to this example:
Therefore,
As you can see that satisfies the first condition of SHM as