To find the restoring force of a spring, we can use Hooke's Law, which states that the force [tex]\( F \)[/tex] exerted by a spring is proportional to the displacement [tex]\( x \)[/tex] and is given by the formula:
[tex]\[ F = -k x \][/tex]
where:
- [tex]\( k \)[/tex] is the spring constant,
- [tex]\( x \)[/tex] is the displacement,
- The negative sign indicates that the force exerted by the spring is in the direction opposite to the displacement.
Given in the problem:
- The spring constant [tex]\( k = 4a \)[/tex],
- The displacement [tex]\( x = 3b \)[/tex].
We plug these values into Hooke's Law:
[tex]\[ F = - (4a) (3b) \][/tex]
Multiplying these values together:
[tex]\[ F = -12ab \][/tex]
Hence, the correct answer is:
C. [tex]\(-12ab\)[/tex]
