Question

current attempt in progress
which one of the following graphs correctly represents the restoring force f of an ideal spring as a function of the displacement x of the spring from its unstrained length?

Explanation:

Step1: Recall Hooke's Law

Hooke's Law states that \(F = -kx\), where \(F\) is the restoring force, \(k\) is the spring constant (\(k>0\)), and \(x\) is the displacement from the un - strained length.

Step2: Analyze the relationship between \(F\) and \(x\)

The equation \(F=-kx\) is a linear equation of the form \(y = mx\) (where \(y = F\), \(m=-k\), and \(x=x\)). When \(x = 0\) (un - strained length), \(F = 0\). The negative sign indicates that the force \(F\) is in the opposite direction of the displacement \(x\). So, the graph of \(F\) versus \(x\) is a straight line passing through the origin with a negative slope.

Answer:

c