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 first determine the equilibrium position of the mass-spring system. The equilibrium position is where the gravitational force pulling the mass downwards is balanced by the elastic force of the spring pulling it upwards.
From the given information, we can calculate the displacement of the spring caused by the added mass.
The unstretched length of the spring is 80 cm, and the length of the spring with the mass suspended at rest is 89 cm. Therefore, the displacement of the spring due to the added mass is:
Displacement = Length with mass - Unstretched length
= 89 cm - 80 cm
= 9 cm
Next, the mass is pulled down an additional 8 cm. This means that the length of the spring will be stretched by an additional 8 cm compared to the equilibrium position.
Now, to find the amplitude of the resulting oscillation, we need to add the displacement due to the added mass to the additional displacement caused by pulling down the mass.
Amplitude = Displacement due to added mass + Additional displacement
= 9 cm + 8 cm
= 17 cm
Therefore, the amplitude of the resulting oscillation is 17 cm.