Question

1.)In a linear oscillation motion, where we are measuring the stiffness constant of the spring, how would you estimate the uncertainty in the equilibrium position?

2.)every spring has different elasticity when validating the hooke's law, how could you identify when the spring is elastic?

Answer 1

Part 1

No physical quantity (length, mass, temperature, etc.) can be measured with complete certainty. By taking great care you may be able to reduce uncertainties until they are extremely small, but not eliminate them entirely.

If you want to measure the uncertainty in the equilibrium position. A ruler calibrated in centimeters can be used for this, but it is highly unlikely that the balance position exactly matches one of the ruler's graduation lines. Thus, the measurement error will be of the order of 1 centimeter. To minimize the error, you could think about getting a tape measure calibrated in millimeters, but again if the balance position does not coincide with one of the graduation lines, the error would be 1 millimeter. If you want to be more precise, you could try to measure the equilibrium position using a laser interferometer, but even in this case the uncertainty will be of the order of the wavelength of the light (0.5 × 10−6?).

The aforementioned determines the uncertainty in a direct measurement, and is given by the appreciation of the instrument that is used in the measurement. For indirect measurement of uncertainty, proceed as follows:

The force of a spring is expressed by the following equation:

Solving the previous equation for x, the equilibrium position of the spring can be determined.

if we assume that the spring is hanging, the force is given by:

and the uncertainty is given by the following equation:

Part 2

Within the elastic zone Hooke's law is fulfilled. The deformations are proportional to the stresses: F =- k x. If the force is withdrawn the spring recovers its original length

If the force is sufficient, the deformations become permanent. Technically the spring is destroyed. In other words the spring will be elastic if a force is no longer applied and the spring returns to its original position, if this does not happen the spring is no longer elastic.