Total energy of a spring-mass system (harmonic motion)

In summary, the conversation revolves around finding the total energy of a 507g mass oscillating on a spring with an amplitude of 10cm and a spring constant of 20 N/m. After discussing various equations and values, it is determined that the energy at maximum amplitude is 0.1J, which is considered to be correct.
  • #1
Terp
41
0
Hi all. I've this problem and I'm stuck on the part where I have to find the total energy.

Homework Statement


A 507 g mass oscillates with an amplitude of 10 cm on a spring whose spring constant is 20 N/m. At t =0s the mass is 5.0 cm to the right of the equilibrium position and moving to the right.

Homework Equations



E = K + U = (1/2)mvx^2 + (1/2)kx^2

I've already figured out the period to be 1.00s, the angular frequency is 6.28 rad/s, phase constant is -1.05 rad, initial velocity is .544 m/s, and final is .628 m/s. I know all of these to be correct.

The Attempt at a Solution



Using the equation above and plugging numbers in I get:

(1/2)(.507kg)(.544^2) + (1/2)(20Nm)(5.0cm^2) = 250.075J but this online homework thing says it's wrong. Should I use E = (1/2)m*vmax^2? That only gives .09J.

Anybody have any clue? Thanks a lot!
 
Last edited:
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  • #2
Check your units.
 
  • #3
Thanks for the reply. I noticed that the 5.0cm isn't in meters, I changed it to .05m, which changed the resulting energy to 0.100J, but that seems low.
 
  • #4
Terp said:
I noticed that the 5.0cm isn't in meters, I changed it to .05m, which changed the resulting energy to 0.100J, but that seems low.
Why not choose another point to compare? Hint: Find the energy when it's at max amplitude.
 
  • #5
That would mean E = 1/2kA^2 = (1/2)*20*.10^2 = .1J. Does that sound correct? It seems too small to be correct.

EDIT: Now that I think about it, .5kg isn't very heave and .544 m/s is pretty darn slow.
 
Last edited:
  • #6
Sounds good to me!
 
  • #7
That was right, thanks a lot! I feel like a tard now! :)
 

What is the equation for calculating the total energy of a spring-mass system?

The total energy of a spring-mass system can be calculated using the equation E = 1/2 * k * x^2, where k is the spring constant and x is the displacement from equilibrium.

How does the total energy of a spring-mass system change as the amplitude increases?

The total energy of a spring-mass system increases as the amplitude increases. This is because the amplitude is directly proportional to the displacement, and the total energy is dependent on the displacement.

Does the total energy of a spring-mass system remain constant over time?

Yes, the total energy of a spring-mass system remains constant over time. This is because in a conservative system, energy is conserved and can only be transferred between different forms of energy.

What happens to the total energy of a spring-mass system if the mass or the spring constant is doubled?

If the mass is doubled, the total energy of the spring-mass system will also double. However, if the spring constant is doubled, the total energy will quadruple. This is because the total energy is directly proportional to both the mass and the spring constant.

Can the total energy of a spring-mass system be negative?

No, the total energy of a spring-mass system cannot be negative. This is because energy is a scalar quantity and cannot have a negative value. However, the potential energy of a spring-mass system can be negative if the spring is stretched beyond its equilibrium position.

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