In a mass-spring system executing simple harmonic motion, the frequency is determined by the properties of the system and remains constant as long as other factors remain unchanged. Therefore, if the amplitude is increased four times, the frequency of the system will remain the same.
The frequency (f) of a mass-spring system can be calculated using the following formula:
f = 1 / (2π) * sqrt(k / m)
Where: f = frequency k = spring constant m = mass of the object attached to the spring
The amplitude (A) does not directly affect the frequency of the system. It only affects the maximum displacement or distance traveled by the object during its oscillations. Increasing the amplitude will result in larger swings or displacements, but it will not change the frequency.
Therefore, if the amplitude of a mass-spring system executing simple harmonic motion is increased four times, the frequency will remain the same.