Aspring has an unstretched length of 10 cm. it exerts a restoring force f when stretched to a length of 11 cm. a. for what length of the spring is its restoring force 3f? b. at what compressed length is the restoring force 2f?

x₀ = unstretched length of spring = 10 cm

x' = stretched length = 11 cm

k = spring constant of the spring

F = restoring force when stretched length is x'

restoring force when stretched length is x'  is given as

F = k (x' - x₀)

F = k (11 - 10)

F = k

(a)

x'' = stretched length

F'' = restoring force when stretched length is x'' = 3F

restoring force when stretched length is x'' is given as

F'' = k (x'' - x₀)

3F = F (x'' - 10)

x''= 13 cm

(b)

x''' = compressed length

F''' = restoring force when compressed length is x'' = 2F

restoring force when  when compressed length is x'' is given as

F''' = k (x₀ - x''' )

2F = F (10 - x''' )

x''' = 8 cm