The following pre-lab questions should help provide you guidance in exploring mass-spring simple harmonic oscillator. 1. For a spring-mass system displaced from equilibrium, F = ma = m" d²y :-kAy where k is the spring constant. A. Substituting y(t) = A cos(@t + 4) and setting y, = 0, solve for angular frequency, w. Consider this equation for the angular frequency of the spring-mass system. How would you expect w to change if you vary the amplitude, the mass, or the spring constant parameters (changing only one parameter at a time). Explain your predictions. B. If you measure the frequency of oscillation, f, for different masses suspended on the same spring what values would you use to plot a graph in order to determine spring constant, k? Hint: lIdeally, you want to analyze a linear graph. What do you need to do with your data to be able to do so? Prepare a table for taking measurements.
The following pre-lab questions should help provide you guidance in exploring mass-spring simple harmonic oscillator. 1. For a spring-mass system displaced from equilibrium, F = ma = m" d²y :-kAy where k is the spring constant. A. Substituting y(t) = A cos(@t + 4) and setting y, = 0, solve for angular frequency, w. Consider this equation for the angular frequency of the spring-mass system. How would you expect w to change if you vary the amplitude, the mass, or the spring constant parameters (changing only one parameter at a time). Explain your predictions. B. If you measure the frequency of oscillation, f, for different masses suspended on the same spring what values would you use to plot a graph in order to determine spring constant, k? Hint: lIdeally, you want to analyze a linear graph. What do you need to do with your data to be able to do so? Prepare a table for taking measurements.
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![The following pre-lab questions should help provide you guidance in exploring mass-spring simple
harmonic oscillator.
1. For a spring-mass system displaced from equilibrium,
d²y
F = ma = m-
dt?
:-kAy
where k is the spring constant.
A. Substituting y(1) = A cos(@t + 4) and setting y, = 0, solve for angular frequency, w.
Consider this equation for the angular frequency of the spring-mass system. How would
you expect w to change if you vary the amplitude, the mass, or the spring constant
parameters (changing only one parameter at a time). Explain your predictions.
B. If you measure the frequency of oscillation, f, for different masses suspended on the
same spring what values would you use to plot a graph in order to determine spring
constant, k? Hint: Ideally, you want to analyze a linear graph. What do you need to do with
your data to be able to do so? Prepare a table for taking measurements.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd995525-d253-4921-8ccc-4f78fb9f767e%2F18e6240e-57ea-4e97-9352-21e88809f0bd%2Fipzk4ja_processed.png&w=3840&q=75)
Transcribed Image Text:The following pre-lab questions should help provide you guidance in exploring mass-spring simple
harmonic oscillator.
1. For a spring-mass system displaced from equilibrium,
d²y
F = ma = m-
dt?
:-kAy
where k is the spring constant.
A. Substituting y(1) = A cos(@t + 4) and setting y, = 0, solve for angular frequency, w.
Consider this equation for the angular frequency of the spring-mass system. How would
you expect w to change if you vary the amplitude, the mass, or the spring constant
parameters (changing only one parameter at a time). Explain your predictions.
B. If you measure the frequency of oscillation, f, for different masses suspended on the
same spring what values would you use to plot a graph in order to determine spring
constant, k? Hint: Ideally, you want to analyze a linear graph. What do you need to do with
your data to be able to do so? Prepare a table for taking measurements.
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