In simple harmonic motion (SHM), the spring constant is really important for figuring out how often something vibrates or moves back and forth.

The spring constant is shown as (k), and it tells us how stiff the spring is.

• If the spring constant (k) is high, it means the spring is very stiff.
• If (k) is low, the spring is more stretchy.

Key Ideas:

• Frequency ((f)) is how many times something moves back and forth in one second.
• Frequency depends on two main things:
  • The mass ((m)) of the object that hangs on the spring.
  • The spring constant ((k)).

How to Calculate Frequency:

You can find the frequency of the oscillation with this formula:

$f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$

Examples:

1. If you use a stiffer spring (with a higher (k)) and keep the same mass, the system will move up and down faster. This means a higher frequency.

2. On the other hand, if you add more mass but keep the spring constant the same, the frequency goes down. So, the movements get slower.

Understanding how mass and spring constant work together helps us learn about how things move in systems that bounce or swing!