How is Vmax Derived as 2πfA from Given Formulae?

[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?

 

[OlderDan]

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?

You need to use carriage returns to put equations on separate lines. Extra spaces do not get included in posts.

Start with 2(pi)(frequency)(Amplitude) and square it. Then make substitions.

 

[Kurdt]

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