# Prove Vmax: 2πfA from Formulae

• quickslant
In summary, the maximum speed (Vmax) of a mass on a spring can be calculated using the formula 2(pi)(frequency)(Amplitude). This can be proven by using the equations (constant k) A^2 = mv^2 + (constant k) x^2 and ma = -(constant k)(x), and substituting in the values for frequency, amplitude, and mass. By making proper substitutions and using simplification, the formula 2(pi)(frequency)(Amplitude) can be derived.
quickslant
Given the following formulaes prove that maximum speed (Vmax) of a mass on a spring is given by 2(pi)(frequency)(Amplitude)

(constant k) A^2 = mv^2 + (constant k) x^2 ma = -(constant k)(x)

f = 1/2(pi) sqrt (a/-x) and f = 1/2(pi) sqrt (constant k/m)

i just don't see how i can make it work... any suggestions?

quickslant said:
Given the following formulaes prove that maximum speed (Vmax) of a mass on a spring is given by 2(pi)(frequency)(Amplitude)

(constant k) A^2 = mv^2 + (constant k) x^2

ma = -(constant k)(x)

f = 1/2(pi) sqrt (a/-x)

f = 1/2(pi) sqrt (constant k/m)

i just don't see how i can make it work... any suggestions?

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Last edited:
What happens to the amplitude when the velocity is at its maximum?

## What does the formula Vmax = 2πfA represent?

The formula Vmax = 2πfA represents the maximum velocity of a particle in simple harmonic motion, where Vmax is the maximum velocity, f is the frequency of motion, and A is the amplitude of motion.

## How is the formula Vmax = 2πfA derived?

The formula Vmax = 2πfA is derived from the equations of simple harmonic motion, which describe the motion of an object back and forth in a straight line with a constant frequency and amplitude. It is based on the relationship between the velocity and displacement of the object.

## What units should be used for the variables in the formula Vmax = 2πfA?

The units for Vmax are typically in meters per second (m/s), the units for f are in hertz (Hz) or cycles per second, and the units for A are in meters (m).

## Can the formula Vmax = 2πfA be used for any type of motion?

No, the formula Vmax = 2πfA is specifically for describing the maximum velocity in simple harmonic motion. It should not be used for other types of motion, such as linear or circular motion.

## How is the formula Vmax = 2πfA useful in scientific research?

The formula Vmax = 2πfA is useful in scientific research as it allows for the calculation of the maximum velocity of a particle in simple harmonic motion, which is a common type of motion in various systems. This formula can be used to analyze and predict the behavior of particles in oscillating systems, making it a valuable tool in many fields such as physics, engineering, and biology.

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