Suppose a ball with mass m hangs vertically from a spring with stiffness k and relaxed length l0. at what length leq will the ball encounter equilibrium?

At equilibrium, the sum of vertical forces are equal to zero. Let's analyze the downward and upward components of the forces.

Downward forces: (Gravity)( is the gravitational constant.)

Upward forces: (Spring)

Equilibrium condition: .

so

Explanation:

If there is no masses hanging from the spring, the length of the spring is equal to . When there is a mass M hanging, the spring will be stretched by an amount of . This distance can be found by using the equilibrium condition, that the sum of the forces is equal to zero.

layers of the earth affect the waves and these effects are seen on instruiments such as seimometers