The total mechanical energy of a spring - mass system in simple harmonic motion is 𝐸=12𝑚𝜔2𝐴2. Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude 𝐴 remains the same. The new mechanical energy will
Question
The total mechanical energy of a spring - mass system in simple harmonic motion is 𝐸=12𝑚𝜔2𝐴2. Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude 𝐴 remains the same. The new mechanical energy will
Solution
The total mechanical energy of a spring-mass system in simple harmonic motion is given by the equation E = 1/2 mω²A².
In this equation:
- E is the total mechanical energy
- m is the mass of the particle
- ω is the angular frequency
- A is the amplitude of the motion
If the mass m is replaced by a particle of double the mass, the new mass will be 2m.
Substituting this into the equation gives the new total mechanical energy as E' = 1/2 * 2m * ω² * A² = mω²A².
So, the new mechanical energy will be double the original energy.
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