A block of mass 200 grams is connected to a light, horizontal spring of spring constant k = 5 N/m. It is free to oscillate on a horizontal, frictionless surface, and we neglect the effect of air resistance throughout. What is the total energy of the harmonic oscillator?

The total energy of a harmonic oscillator is given by the formula:

\[
E = \frac{1}{2} k A^2
\]

where:
- \( E \) is the total energy,
- \( k \) is the spring constant,
- \( A \) is the amplitude of oscillation.

However, the amplitude \( A \) is missing in the problem statement. Without the amplitude, we cannot directly calculate the total energy. 

If you know the amplitude, you can plug it into the formula to find the total energy.

Would you like to provide the amplitude, or should we approach the problem from a different angle? Let me know if you have questions!

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Here are 5 related questions to explore this further:
1. What is the amplitude of oscillation, and how does it affect the energy of the system?
2. How can we calculate the maximum velocity of the block in harmonic motion?
3. How would the total energy change if the spring constant doubled?
4. What is the relationship between total energy and the frequency of oscillation?
5. How does the total energy relate to the potential and kinetic energy at different points in the motion?

**Tip:** In harmonic oscillation, the total mechanical energy remains constant and is shared between kinetic and potential energy, depending on the position of the mass during its motion.

Understand how to calculate the total energy of a harmonic oscillator connected to a spring. This problem involves a spring constant k = 5 N/m and a block of mass 200 grams on a frictionless surface. Learn the formula E = (1/2) k A^2 and the importance of amplitude in the calculation. Suitable for students in Grades 10-12.

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