In Simple Harmonic Motion (SHM), the maximum speed, often referred to as the peak or amplitude speed, is determined using the formula:

where $\omega$ represents the angular frequency and $A$ signifies the amplitude of the motion.

The maximum speed occurs when the object is at its equilibrium position. This is because the object in SHM moves fastest at this midpoint and experiences the slowest motion at the extremes of its oscillation.

To elaborate, the angular frequency $\omega$ is related to the period $T$ of the motion—the time taken for one complete cycle—and is calculated using the formula:

This angular frequency quantifies how rapidly the object oscillates back and forth.

The amplitude $A$ indicates the maximum displacement of the object from its equilibrium position, defining how far the object travels from its midpoint during each cycle of oscillation.

By multiplying the angular frequency by the amplitude, we can ascertain the maximum speed of the object in SHM. This relationship highlights that the object’s speed is directly proportional to both the rate of oscillation (angular frequency) and the extent of its movement during each oscillation (amplitude).

It is crucial to understand that this formula provides the maximum speed, not the speed at every point in the motion. The speed of an object in SHM varies throughout its cycle, reaching its peak at the equilibrium position and dropping to zero at the extremes of its path. However, knowing the maximum speed is invaluable for analyzing the overall behavior of the system in SHM.

IB Physics Tutor Summary: To calculate the maximum speed in Simple Harmonic Motion (SHM), utilize the formula:

In this context, $\omega$ is the angular frequency, given by $\omega = \frac{2\pi}{T}$ (where $T$ is the period), and $A$ is the amplitude, which represents the distance the object moves from its central position. The maximum speed occurs at the central point of the motion, providing insight into the object’s fastest movement during SHM.