1. The problem statement, all variables and given/known data When a mass m is placed on the end of a spring in the vertical position, it stretches the spring a distance d. Find the spring constant k. 2. Relevant equations Force of a spring = Fs = -ky Elastic Potential Energy = Us= (1/2)ky^2 Gravitational Potential Energy = Ug = mgy 3. The attempt at a solution Method 1 - Conservation of total mechanical energy. When the spring is not streched, the mass has only gravitational potential energy Ug=mgd. After the spring drops a distance d, the mass has only elastic potential energy. Hence mgd = (1/2)kd^2 or k = 2mg/d Method 2 - Newton's second law. When the mass has dropped a distance d, it has streched the string a distance d. Hence the sum of the forces in the vertical position gives Fs -Fg=0 or kd-mg=0 or k=mg/d My question is, why do these two methods give different values? Thank you.