A spring hanging from the ceiling has an unstretched length of 80 cm. A mass is then suspended at rest from the spring causing its length to increase to 89 cm. The mass is pulled down an additional 8 cm and released. What is the amplitude of the resulting oscillation?

To find the amplitude of the resulting oscillation, we need to understand the behavior of a mass-spring system.

When a mass is attached to a spring, it obeys Hooke's Law, which states that the force exerted by the spring is directly proportional to the displacement of the mass from its equilibrium position. Mathematically, this relationship can be represented as F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.

In this case, we know that the unstretched length of the spring is 80 cm, and when the mass is suspended from the spring, its length increases to 89 cm. To find the displacement from the equilibrium position, we need to subtract the unstretched length from the new length: 89 cm - 80 cm = 9 cm.

Now, when an additional 8 cm is pulled down and released, the spring will oscillate around the equilibrium position. The amplitude of the resulting oscillation is equal to half the total displacement. In this case, the total displacement is 8 cm, so the amplitude is 1/2 * 8 cm = 4 cm.

Therefore, the amplitude of the resulting oscillation is 4 cm.

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