In regards to Period of a Mass on a Spring, If the amplitude of the oscillation is increased, would the oscillation period be unchanged? Is so, is it because the oscillator's period is determined only by the stiffness of the spring and the mass of the block?
The period of a mass on a spring does change if the amplitude of the oscillation is increased. The period of an oscillator is not solely determined by the stiffness of the spring and the mass of the block, but also affected by the amplitude.
To understand why the period changes with amplitude, let's first discuss what the period represents. The period is the time it takes for one complete oscillation, which consists of the mass moving from one extreme (e.g., maximum displacement to the left) to the other extreme (e.g., maximum displacement to the right) and back again.
When the amplitude of the oscillation is increased, it means that the mass is being displaced over a greater distance from its equilibrium position. As the amplitude increases, the mass has to cover a longer distance in the same amount of time to complete one oscillation.
To visualize this, imagine swinging on a swing. When you push yourself to swing higher (increasing the amplitude), you have to exert more force and energy to cover a longer distance from one end of the swing to the other.
Similarly, in the case of a mass on a spring, when the amplitude is increased, the mass needs more time to cover the increased distance of its oscillation. Consequently, the period lengthens, and it takes more time for the mass to complete one oscillation.
So, to summarize, the oscillation period of a mass on a spring is not solely determined by the stiffness of the spring and the mass of the block. It is also affected by the amplitude of the oscillation: increasing the amplitude leads to a longer period, while decreasing the amplitude leads to a shorter period.