Energy of the Simple Harmonic Oscillator

[adashiu]

A 50.0-g mass connected to a spring with a force constant
of 35.0 N/m oscillates on a horizontal, frictionless
surface with an amplitude of 4.00 cm. Find the speed of the mass
when the displacement is 1.00 cm.

Can I use here something like :

\frac{mv2}{2}=0,5kx²?

 

[Doc Al]

Use conservation of energy. What's the total energy at any point in the motion?

 

[adashiu]

The total energy is 0,5kA²=0,028

But how to express an energy at displacement 1cm?

 

[Doc Al]

Hint: Total mechanical energy is the sum of kinetic and potential energy.

 

[adashiu]

Yes i know that but there is no formula with velocity...

I've got to use mv2/2??

 

[Doc Al]

Yes i know that but there is no formula with velocity...

I've got to use mv2/2??

Yes, that's the kinetic energy. What's the potential energy at any point?

 

[adashiu]

Potential energy is 0?

 

[Doc Al]

Potential energy is 0?

Total energy is : 0,5kA²=4*10^-5

mv2²/2=4*10^-5

v=0.04, of course it seems not to be correct :(

No. Hint: Potential energy is zero when x = 0 and maximum at x = A. What's the PE at an arbitrary position?

 

[valjok]

\frac{mv2}{2}=0,5kx²


?

Your equation defines a condition when a half of the energy is in speed and another half in the displacement.
E_k + E_p = E
E = kA²/2
mv²/2 = E - kx²/2