Hooke’s Law. According to Hooke’s law for springs, developed by Robert Hooke (1635–1703), the force exerted by a spring that has been compressed to a length x is given by the formula F = −k(x − x0), where x0 is the natural length of the spring and k is a constant, called the spring constant. A certain spring exerts a force of 50 N when compressed to a length of 5 cm and a force of 20 N when compressed to a length of 10 cm ft. For this spring, find the following.

a. The linear equation that relates the force exerted to the length compressed

b. The spring constant

c. The natural length of the spring