Here's why:
* Simple Harmonic Motion: This type of motion is characterized by a restoring force that is proportional to the displacement from equilibrium. Examples include a mass on a spring or a pendulum swinging with small angles.
* Maximum Speed: The maximum speed of a simple harmonic oscillator occurs when it passes through its equilibrium position.
* Energy: The total energy of a simple harmonic oscillator is constant and is related to both the amplitude and the maximum speed. The energy is proportional to the square of the amplitude and also proportional to the square of the maximum speed.
Therefore, doubling the amplitude will quadruple the total energy. Since the energy is also proportional to the square of the maximum speed, doubling the amplitude will double the maximum speed.
Other ways to double the maximum speed:
* Changing the Spring Constant: For a mass on a spring, increasing the spring constant (making the spring stiffer) will increase the restoring force. This will lead to a higher maximum speed, but you'll need to find the exact factor by which to increase the spring constant to achieve a doubling of the maximum speed.
* Changing the Mass: For a mass on a spring, decreasing the mass will also increase the maximum speed. Again, you'll need to find the exact factor by which to decrease the mass to achieve a doubling of the maximum speed.
Important Note: These are general principles. The specific calculations to determine the exact changes needed to double the maximum speed will depend on the specific details of the simple harmonic oscillator system (e.g., the mass, spring constant, or length of the pendulum).
