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Hello everyone, I hope someone can help me with this simple harmonic motion question

I've been trying it for about an hour now and I think i may have found the problem but I want to run it by someone else :)

I'm taking this Phsyics 12U course (Uni prep for Ontario, Canada) through correspondence and all I have to go by are the work books that I have received.

My work book gives me a bunch of formulas for harmonic motion, those formulas are what I am using to re-arrange and sub and so on.

So after re-arranging and all that fun stuff I get as far as

===============================================

so now the speed of the mass will be at max when it is right at equilibrium (x = 0)

and the potential energy will be zero and the kinetic energy will be max

So then I get this formula using energy equations, (Ek = kinetic energy, m = mass)

vmax = sqrt(2 * Ek / m)

now we can get Ek another way, and that is using the total energy of the system equation and this is where i get hung up

in my workbook, it has the total energy of the system as

the total energy is all kinetic in this case so we can sub Ek for Et

so I try to plug that into

vmax = sqrt(2 * Ek / m)

and I end up with

which kind of looks like the 2 * pi * f * A rearranged except for that useless 2 in the numerator! :@

so then I research this using google and on wikipedia it has the total energy of a spring mass system as

so this formula has the same thing except the 2 in the denominator

I then check another site and it also has the 2 in the denominator

and it clicks, i put this formula in the equation instead and it all works out!

so is my workbook giving me bad information??

is the total energy of a Spring Mass system given as

or

???

thanks in advance for all of the help!

I've been trying it for about an hour now and I think i may have found the problem but I want to run it by someone else :)

I'm taking this Phsyics 12U course (Uni prep for Ontario, Canada) through correspondence and all I have to go by are the work books that I have received.

## Homework Statement

My work book gives me a bunch of formulas for harmonic motion, those formulas are what I am using to re-arrange and sub and so on.

**Prove that Max Speed of a mass on a spring is given by 2 * pi * f * A**So after re-arranging and all that fun stuff I get as far as

**vmax= sqrt(k/m) * A**===============================================

so now the speed of the mass will be at max when it is right at equilibrium (x = 0)

and the potential energy will be zero and the kinetic energy will be max

So then I get this formula using energy equations, (Ek = kinetic energy, m = mass)

vmax = sqrt(2 * Ek / m)

now we can get Ek another way, and that is using the total energy of the system equation and this is where i get hung up

in my workbook, it has the total energy of the system as

**Et = kA^2**the total energy is all kinetic in this case so we can sub Ek for Et

so I try to plug that into

vmax = sqrt(2 * Ek / m)

and I end up with

**sqrt(2k/m) * A**

which kind of looks like the 2 * pi * f * A rearranged except for that useless 2 in the numerator! :@

so then I research this using google and on wikipedia it has the total energy of a spring mass system as

**Et = (kA^2) / 2**so this formula has the same thing except the 2 in the denominator

I then check another site and it also has the 2 in the denominator

and it clicks, i put this formula in the equation instead and it all works out!

so is my workbook giving me bad information??

is the total energy of a Spring Mass system given as

**Et = (k * A^2)**or

**Et = (K * A^2) / 2**???

thanks in advance for all of the help!

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