How do you calculate the maximum speed in SHM?

The maximum speed in Simple Harmonic Motion (SHM) is calculated using the formula v_max = ωA, where ω is the angular frequency and A is the amplitude.

In Simple Harmonic Motion (SHM), the maximum speed, also known as the peak or amplitude speed, occurs when the object is at the equilibrium position. This is because the object in SHM moves fastest when it is at the midpoint of its motion, and slowest at the extremes. The formula to calculate this maximum speed is v_max = ωA.

In this formula, ω represents the angular frequency of the motion. The angular frequency is related to the period of the motion (the time it takes for one complete cycle) and is calculated as ω = 2π/T, where T is the period. The angular frequency essentially describes how quickly the object is oscillating back and forth.

A, on the other hand, represents the amplitude of the motion. The amplitude is the maximum displacement of the object from its equilibrium position. It essentially describes how far the object moves from its midpoint during each oscillation.

By multiplying the angular frequency by the amplitude, we can calculate the maximum speed of the object in SHM. This is because the speed of the object is directly proportional to both how quickly it is oscillating (the angular frequency) and how far it is moving during each oscillation (the amplitude).

It's important to note that this formula gives the maximum speed, not the speed at any given point in the motion. The speed of an object in SHM varies throughout its motion, being maximum at the equilibrium position and zero at the extremes of the motion. However, knowing the maximum speed can be very useful in understanding and analysing the overall behaviour of the object in SHM.

IB Physics Tutor Summary: To find the maximum speed in Simple Harmonic Motion (SHM), use the formula v_max = ωA. Here, ω is the angular frequency (ω = 2π/T, where T is the period), and A is the amplitude, or how far the object moves from its central point. The max speed occurs at the central point of the motion, helping us understand the object's fastest movement in SHM.