Question

How does increasing amplitude affect frequency in simple harmonic motion?

Answer 1

In simple harmonic motion (SHM), the amplitude refers to the maximum displacement from the equilibrium position that an oscillating object reaches. The frequency, on the other hand, represents the number of complete oscillations or cycles that occur per unit of time.

In SHM, the amplitude does not affect the frequency of the motion. The frequency of an object undergoing SHM is determined solely by the characteristics of the system, such as the mass and the stiffness (or spring constant) of the system.

The frequency of SHM can be calculated using the formula:

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

where:

• $f$ is the frequency of the motion,
• $\pi$ is a mathematical constant approximately equal to 3.14159,
• $k$ is the spring constant, and
• $m$ is the mass.

As you can see from the formula, the frequency depends only on the spring constant and the mass, and not on the amplitude of the motion.

Increasing the amplitude of the oscillation in SHM will not change the frequency. It will only affect the maximum displacement or the range over which the object oscillates. The object will still complete the same number of oscillations per unit of time, regardless of whether the amplitude is increased or decreased.