In simple harmonic motion, the acceleration of an object undergoing oscillation is directly proportional to the displacement from the equilibrium position. When the amplitude of the motion doubles, i.e., when the displacement from the equilibrium position is doubled, the acceleration of the object also doubles.
Mathematically, the acceleration (a) in simple harmonic motion is given by the equation:
a = -ω²x
where ω represents the angular frequency and x represents the displacement from the equilibrium position.
In this equation, we can see that the acceleration (a) is directly proportional to the displacement (x). Therefore, when the amplitude (magnitude of displacement) doubles, the displacement (x) also doubles. As a result, the acceleration (a) will double as well.
It's important to note that the direction of acceleration in simple harmonic motion is always opposite to the direction of displacement. The negative sign in the equation indicates this relationship, implying that the acceleration and displacement are in opposite directions.