Suppose a spring with a spring constant of 10 N/m is suspended vertically in an oil with a coefficient of drag b-0.7 N m/s. A mass of 3 kg is suspended from the spring and the spring is compressed until the mass is 10 cm above the equilibrium point, then released from rest. A. Where is the mass after 12 s? B. Draw a graph of the position vs time for the mass on the spring. Your graph should match the result you obtained in part a. Remember to include labels and units.
Suppose a spring with a spring constant of 10 N/m is suspended vertically in an oil with a coefficient of drag b-0.7 N m/s. A mass of 3 kg is suspended from the spring and the spring is compressed until the mass is 10 cm above the equilibrium point, then released from rest. A. Where is the mass after 12 s? B. Draw a graph of the position vs time for the mass on the spring. Your graph should match the result you obtained in part a. Remember to include labels and units.
Transcribed Image Text:**Title: Spring-Mass System with Damping**
**Problem Statement:**
Suppose a spring with a spring constant of 10 N/m is suspended vertically in an oil with a coefficient of drag \( b = 0.7 \) N·s/m. A mass of 3 kg is suspended from the spring and the spring is compressed until the mass is 10 cm above the equilibrium point, then released from rest.
**Questions:**
A. Where is the mass after 12 seconds?
B. Draw a graph of the position vs. time for the mass on the spring. Your graph should match the result you obtained in part A. Remember to include labels and units.
**Explanation:**
In this problem, we are dealing with a damped harmonic oscillator. The equilibrium position is where the forces on the mass balance. When the mass is displaced from this position and released, it will oscillate. Due to the presence of damping (the oil's drag), the amplitude of the oscillations will gradually decrease over time.
When solving for the position of the mass, consider the damping factor present in the environment. Use the formulas and methods suitable for calculating the position of a damped harmonic oscillator at a given time.
**Graph Description:**
When creating the graph of the position vs. time:
- The x-axis should represent time (t) in seconds.
- The y-axis should represent the position (displacement) of the mass in meters.
- Include negative values in your y-axis to depict oscillation below the equilibrium point.
- The graph should show a sinusoidal wave that gradually decreases in amplitude over time due to damping, eventually settling toward the equilibrium position.
The position will be calculated and plotted over the 12-second interval to match the results obtained in question A.
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