# Energy of the Simple Harmonic Oscillator

1. Jan 3, 2009

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

????

2. Jan 3, 2009

### Staff: Mentor

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

3. Jan 3, 2009

The total energy is 0,5kA2=0,028

But how to express an energy at displacement 1cm?

4. Jan 3, 2009

### Staff: Mentor

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

5. Jan 3, 2009

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

I've got to use mv2/2??

6. Jan 3, 2009

### Staff: Mentor

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

7. Jan 3, 2009

Potential energy is 0?

8. Jan 3, 2009

### Staff: Mentor

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

9. Jan 3, 2009

### valjok

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