Final answer:
The spring gradient, denoted by the force constant (k), signifies the ratio of applied force to displacement (F/x). With an initial 50.0 cm displacement, the force constant is calculated as k = F/50.0 cm. However, determining the effective mass of the spring (m) requires additional information, specifically the force applied and acceleration due to gravity.
Step-by-step explanation:
The gradient of a spring, denoted by the force constant (k), signifies the ratio of applied force to displacement (F/x).
The formula, k = F/x, defines this relationship, where F is the applied force and x is the displacement produced.
For a spring with an initial 50.0 cm displacement, the force constant (k) is determined as F/50.0 cm.
However, to calculate the effective mass of the spring (m), additional information is required.
Effective mass (m) is the equivalent mass of an object exhibiting the same spring behavior, calculated by m = k/g, where g is the acceleration due to gravity.
The absence of force applied and acceleration due to gravity values prevents the determination of effective mass.