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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, 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.
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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