Simple harmonic motion oscillate. What is the total energy

In summary, the total energy of the oscillating mass with a position given by x(t)=(2.0cm)cos(10t−π/4) is 0.001J. This can be found by calculating the amplitude of the velocity, which is used to find the maximum kinetic energy, which is equal to the total energy since there is no potential energy at that moment.
  • #1
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Homework Statement


The position of a 50 g oscillating mass is given by x(t)=(2.0cm)cos(10t−π/4), where t is in s. If necessary, round your answers to three significant figures. Determine: The total energy.

Homework Equations


T = 2π/w
T = 2π√m/k
1/2kA^2
1/2mv^2
1/2kx^2

The Attempt at a Solution


T = 2π/10 = 0.6283s
k = 0.5kg / (0.6823/2π)^2 = 5.000N/m
1/2kA^2 = 0.5(5)(0.02)^2 = 0.001J
 
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  • #2
Your answer is right.

In my opinion, it's more straightforward to find the answer from the maximum kinetic energy. Find the amplitude of dx/dt, which is the maximum velocity, which can be used to find the maximum kinetic energy (which equals the total energy because at that moment there's no potential energy).

But whichever way you like best is good.
 
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1. What is simple harmonic motion oscillation?

Simple harmonic motion oscillation is a type of motion where an object moves back and forth in a regular pattern around a central equilibrium point. This type of motion is often seen in pendulums, springs, and other oscillating systems.

2. How is simple harmonic motion different from other types of motion?

Simple harmonic motion is characterized by its regular and predictable pattern of oscillation. This is in contrast to other types of motion, such as linear motion, where the object moves in a straight line, or circular motion, where the object moves in a circular path.

3. What factors affect the frequency of simple harmonic motion oscillation?

The frequency of simple harmonic motion oscillation is affected by the mass of the object, the stiffness of the spring or pendulum, and the amplitude (maximum displacement) of the oscillation. The frequency is also inversely proportional to the square root of the object's mass.

4. How is the total energy of a system in simple harmonic motion calculated?

The total energy of a system in simple harmonic motion is the sum of its kinetic energy and potential energy. The kinetic energy is equal to 1/2 times the mass of the object times the square of its velocity. The potential energy is equal to 1/2 times the spring constant times the square of the displacement from the equilibrium point.

5. Can the total energy of a system in simple harmonic motion change?

No, the total energy of a system in simple harmonic motion remains constant. This is because the potential energy and kinetic energy are constantly exchanging back and forth as the object oscillates. Therefore, the total energy remains the same throughout the motion.

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