PHYS-302, Physics of Waves (Summer 2007)

Introduction to Oscillation

During our first two-hour class period we investigated the fundamentals of simple oscillation. Mixed in with some lecture material (where we derived the equation of motion and discussed the various forms of mathematical and physical solutions for oscillation) and interaction with some computer animations and JAVA applets, the 12 students were separated into four groups and spent approximately half an hour investigating four different aspects of oscillatory motion with a mass-spring system. The students were given approximately 20 minutes to complete a unique, simple hands-on investigation and then we discussed each group's results together as a class.

Here's a spreadsheet with the student results (and with Dr. Russell's summary).

Ann, Ken and Josh hung various masses from a spring and measured the displacement. After plotting their data, they concluded that the elastic restoring force for a mass-spring system is linearly proportional to the distance the spring is stretched. From a plot of force versus displacement they determined the spring constant of the spring.
Herman, Stephanie and Don measured the period for a mass-spring system by keeping the mass the same, but changing the spring constant. They found that two springs in series provides a more compliant (less stiff) effective spring constant resulting in a longer period, compared to a single spring. They also found that two springs in parallel provide a stiffer effective spring constant resulting in a shorter period.

Joe, Jared and Chris investigated the effect of varying the mass on the resulting period of a mass-spring system. They found that larger mass results in a longer period, but that the relationship is not linear. We also discovered that the effective mass of the spring plays an important role especially when the attached hanging mass is small compared to the spring mass.

Mike and Kurt discovered that, when using a conical spring (nonuniform diameter), the period of a mass-spring system depends on the orientation of the spring. The orientation of the spring affects how much of the spring mass contributes to the "effective mass" of the system. Hanging the spring fat end up results in a larger effective mass and a slightly longer period than when the fat end is down. The effect was more noticable for smaller attached mass.

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Ann, Ken and Josh hung various masses from a spring and measured the displacement. After plotting their data, they concluded that the elastic restoring force for a mass-spring system is linearly proportional to the distance the spring is stretched. From a plot of force versus displacement they determined the spring constant of the spring.
Herman, Stephanie and Don measured the period for a mass-spring system by keeping the mass the same, but changing the spring constant. They found that two springs in series provides a more compliant (less stiff) effective spring constant resulting in a longer period, compared to a single spring. They also found that two springs in parallel provide a stiffer effective spring constant resulting in a shorter period.
Joe, Jared and Chris investigated the effect of varying the mass on the resulting period of a mass-spring system. They found that larger mass results in a longer period, but that the relationship is not linear. We also discovered that the effective mass of the spring plays an important role especially when the attached hanging mass is small compared to the spring mass.
Mike and Kurt discovered that, when using a conical spring (nonuniform diameter), the period of a mass-spring system depends on the orientation of the spring. The orientation of the spring affects how much of the spring mass contributes to the "effective mass" of the system. Hanging the spring fat end up results in a larger effective mass and a slightly longer period than when the fat end is down. The effect was more noticable for smaller attached mass.