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

[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

 

[Dr. Courtney]

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

 

[haruspex]

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

 

[Mary1910]

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

 

[haruspex]

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.

 

[Mary1910]

What's the equation of simple harmonic motion?

Hooke's Law: F=-kx

 

[SammyS]

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