Total energy oscillation problem

In summary, the total energy oscillation problem is a phenomenon where the total energy of a system oscillates between potential and kinetic energy. It is caused by the exchange of energy between these two forms and can be measured by tracking changes in energy over time. This phenomenon has various applications in different fields and can be minimized by reducing external forces, increasing damping, optimizing system design, or using feedback control systems.
  • #1
vande060
186
0

Homework Statement



The displacement of a mass m = 0.01 kg is x(t) = 0.25m sin(62.83t/s − 0.785398) Find its amplitude, its total
energy, and its speed at t = 0.



Homework Equations



E = Av^2 + Bx^2
x = Asin(wt-theta)


The Attempt at a Solution



i use that above formula to find that Amplitude = .25
speed at t = 0 should be the derivative of the x function i think

v(t) = (.25m)(62.83)cos(62.83t/s - 0.785398)
v(0) = (.25m)(62.83)cos(- 0.785398)

I am not sure about the last part there with finding the energy, any suggestions?
 
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  • #2
Total energy = KE + PE

Total energy = (1/2)kA2
 

1. What is total energy oscillation problem?

The total energy oscillation problem is a phenomenon in which the total energy of a system oscillates between potential and kinetic energy. This can occur in various systems, such as mechanical systems, electrical circuits, and even biological systems.

2. What causes total energy oscillation?

Total energy oscillation is caused by a constant exchange of energy between potential and kinetic energy. This exchange occurs due to the nature of the system and the forces acting on it.

3. How is total energy oscillation measured?

Total energy oscillation can be measured by tracking the changes in potential and kinetic energy over time. This can be done through mathematical calculations or by using instruments such as accelerometers or strain gauges.

4. What are the applications of total energy oscillation?

Total energy oscillation has various applications in different fields. In mechanical systems, it can be used to design efficient machines that convert energy from one form to another. In electrical circuits, it can be used to optimize power distribution. It is also important in understanding biological processes, such as muscle contraction and heartbeats.

5. How can total energy oscillation be minimized?

Total energy oscillation can be minimized by reducing the external forces acting on the system, increasing the damping in the system, or by optimizing the design of the system to reduce energy losses. In some cases, it may also be possible to use feedback control systems to stabilize the oscillations.

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