Energy of the Simple Harmonic Oscillator

In summary: E - kx2/2)/mv = sqrt(2(E - kx2/2)/m)In summary, the speed of a 50.0-g mass connected to a spring with a force constant of 35.0 N/m oscillating on a horizontal, frictionless surface with an amplitude of 4.00 cm can be found using the equation v = sqrt(2(E - kx2/2)/m), where E represents total energy, k represents the force constant, x represents displacement, and m represents mass. At a displacement of 1.00 cm, the speed of the mass would be approximately 0.04 m/s.
  • #1
adashiu
21
0
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 :

[tex]\frac{mv2}{2}[/tex]=0,5kx2?
 
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  • #2
Use conservation of energy. What's the total energy at any point in the motion?
 
  • #3
The total energy is 0,5kA2=0,028

But how to express an energy at displacement 1cm? :blushing:
 
  • #4
Hint: Total mechanical energy is the sum of kinetic and potential energy.
 
  • #5
Yes i know that but there is no formula with velocity...

I've got to use mv2/2??
 
  • #6
adashiu said:
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?
 
  • #7
Potential energy is 0?
 
  • #8
adashiu said:
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?
 
  • #9
adashiu said:
[tex]\frac{mv2}{2}[/tex]=0,5kx2


?
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
 

1. What is the Simple Harmonic Oscillator?

The Simple Harmonic Oscillator is a physical system that exhibits oscillatory motion, where the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction of the displacement. It is a fundamental concept in physics and can be seen in many natural phenomena such as the motion of a pendulum or a mass-spring system.

2. What is the energy of a Simple Harmonic Oscillator?

The energy of a Simple Harmonic Oscillator is the sum of its kinetic energy and potential energy. In SHM, the potential energy is directly proportional to the square of the displacement from the equilibrium position, while the kinetic energy is directly proportional to the square of the velocity. As the oscillator moves, the energy is constantly being exchanged between kinetic and potential, but the total energy remains constant.

3. How is the energy of a Simple Harmonic Oscillator calculated?

The energy of a Simple Harmonic Oscillator can be calculated using the equation E= 1/2kx^2, where E is the total energy, k is the spring constant, and x is the displacement from the equilibrium position. This equation takes into account both the potential and kinetic energy. Additionally, the maximum potential energy of a SHO is equal to the maximum kinetic energy, so the total energy can also be calculated as E= 1/2kA^2, where A is the amplitude of the motion.

4. How does the amplitude affect the energy of a Simple Harmonic Oscillator?

The amplitude of a Simple Harmonic Oscillator directly affects the energy of the system. As the amplitude increases, the kinetic energy and potential energy also increase, resulting in a higher total energy. This is because the amplitude is directly proportional to the maximum displacement from the equilibrium position, which is a factor in calculating the energy of a SHO.

5. Can the energy of a Simple Harmonic Oscillator ever be negative?

No, the energy of a Simple Harmonic Oscillator can never be negative. This is because both the kinetic and potential energies are always positive, and the total energy is the sum of these two values. In SHM, energy is constantly being exchanged between kinetic and potential, but the total energy remains constant. Thus, the energy of a SHO will always be a positive value.

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