Questions: A spring with a mass on the end of it hangs in equilibrium a distance of 63.4 cm above the floor. The mass is pulled down a distance 9 cm below the original position, released, and allowed to oscillate. How high above the floor, in cm , is the mass at the highest point in its oscillation? Please round your answer to one decimal place.

A spring with a mass on the end of it hangs in equilibrium a distance of 63.4 cm above the floor. The mass is pulled down a distance 9 cm below the original position, released, and allowed to oscillate. How high above the floor, in cm , is the mass at the highest point in its oscillation? Please round your answer to one decimal place.
Transcript text: A spring with a mass on the end of it hangs in equilibrium a distance of 63.4 cm above the floor. The mass is pulled down a distance 9 cm below the original position, released, and allowed to oscillate. How high above the floor, in cm , is the mass at the highest point in its oscillation? Please round your answer to one decimal place.
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Solution

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Solution Steps

Step 1: Understand the Problem

The problem involves a mass-spring system in equilibrium and its oscillation. Initially, the mass is at an equilibrium position 63.4 cm above the floor. It is then pulled down 9 cm and released, allowing it to oscillate.

Step 2: Determine the Amplitude of Oscillation

The amplitude of oscillation is the maximum displacement from the equilibrium position. Since the mass is pulled down 9 cm from its equilibrium position, the amplitude is 9 cm.

Step 3: Calculate the Highest Point in Oscillation

The highest point in the oscillation occurs when the mass is at its maximum displacement above the equilibrium position. This is equal to the equilibrium position plus the amplitude of oscillation.

\[ \text{Highest point} = \text{Equilibrium position} + \text{Amplitude} = 63.4 \, \text{cm} + 9 \, \text{cm} = 72.4 \, \text{cm} \]

Final Answer

The mass is at a height of \(\boxed{72.4 \, \text{cm}}\) above the floor at the highest point in its oscillation.

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