Finding total energy of an oscillator

In summary, the conversation discusses finding the total energy of an oscillator with a mass of 2 kg, given the equation x=2cos(6∏t). The person attempting to solve the problem suggests using the formula KE = 1/2msquared, but someone else points out that the correct formula to use is v(max)=Aω, with ω being the angular frequency. The correct angular frequency for the given equation is then determined to be 6π.
  • #1
jca90
1
0

Homework Statement



Find the total energy of the following (mass m= 2 kg) oscillator.

Homework Equations



x=2cos(6∏t)


The Attempt at a Solution



Wouldn't I take my Amplitude of 2 and my period of 6 mulitply them together to get my max velocity of 12 then using KE = 1/2msquared I would take 1/2(2)(12)squared to get 144. But this is no where close to being right. My choice are:

A) 1320
B) 1420
C) 1520
D) 1620
E) 1720
F) 1820
 
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  • #2
The simple harmonic motion is described with a function x(t)=Acos(ωt), with ω the angular frequency. The maximum speed is v(max)=Aω. You need ω. What is it if x(t)=2cos(6π t)?

ehild
 

Related to Finding total energy of an oscillator

1. How is the total energy of an oscillator defined?

The total energy of an oscillator is the sum of its kinetic energy and potential energy. Kinetic energy is the energy of motion, while potential energy is the energy stored in a system due to its position or configuration.

2. What is the equation for calculating the total energy of an oscillator?

The equation for calculating the total energy of an oscillator is: E = 1/2 * m * v^2 + 1/2 * k * x^2, where m is the mass of the oscillator, v is its velocity, k is the spring constant, and x is the displacement from equilibrium.

3. How does the total energy of an oscillator change over time?

The total energy of an oscillator remains constant over time if there is no external force acting on it. However, if there is an external force, such as friction, the total energy will decrease over time due to work being done against the force.

4. Can the total energy of an oscillator be negative?

No, the total energy of an oscillator cannot be negative. Kinetic and potential energy are always positive values, and the sum of two positive values will also be positive.

5. How does the amplitude of an oscillator affect its total energy?

The amplitude of an oscillator does not affect its total energy. The total energy is determined by the spring constant, mass, and velocity of the oscillator, not its amplitude. However, a higher amplitude may result in a higher maximum kinetic and potential energy, but the total energy will remain the same.

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