# Max Speed of Mass on Spring: Calculate Vmax with 2πfA

• Mary1910
In summary, to prove that the maximum speed of a mass on a spring is given by 2πfA, one can use the conservation of energy method without calculus. This involves computing the maximum potential energy and setting it equal to the maximum kinetic energy, then solving for velocity. Alternatively, one can use the equation of simple harmonic motion, which involves Hooke's Law (F=-kx) and a sine or cosine term.
Mary1910
Prove that the maximum speed (Vmax) of a mass on a spring is given by 2πfA.

I have no idea how to solve this problem. I have not taken calculus yet, and I am really confused on how to come up with a solution for this. Any help would be appreciated. Thanks

With conservation of energy, you can solve it without Calculus. Compute max potential energy. Set equal to max kinetic energy. Solve for v.

As Dr. Courtney says, but first you need to quote the general equation for the motion.

Ok I'm still lost. Should I be using, E=½mv^2 + ½kx^2 for the general equation for the motion?

Mary1910 said:
Ok I'm still lost. Should I be using, E=½mv^2 + ½kx^2 for the general equation for the motion?
No, that's just conservation of energy in a spring. What's the equation of simple harmonic motion? Or, you can use the above equation if you know the relationship between f, k and m for a spring.

haruspex said:
What's the equation of simple harmonic motion?

Hooke's Law: F=-kx

The general equation of motion should have a sine or cosine in it.

## What is the formula for calculating Vmax in a mass on a spring system?

The formula for calculating Vmax in a mass on a spring system is Vmax = 2πfA, where f is the frequency of the oscillation and A is the amplitude of the oscillation.

## How does amplitude affect the maximum speed of a mass on a spring?

The maximum speed of a mass on a spring is directly proportional to the amplitude of the oscillation. This means that a larger amplitude will result in a higher Vmax.

## What is the relationship between frequency and maximum speed in a mass on a spring system?

The maximum speed of a mass on a spring is directly proportional to the frequency of the oscillation. This means that a higher frequency will result in a higher Vmax.

## Can the maximum speed of a mass on a spring be negative?

No, the maximum speed of a mass on a spring cannot be negative. This is because the formula for Vmax only yields positive values.

## How does the mass of the object on the spring affect the maximum speed?

The mass of the object on the spring does not affect the maximum speed. Vmax is dependent on the frequency and amplitude of the oscillation, not the mass of the object.

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