(II) A mass m on a frictionless surface is attached to

Chapter , Problem 93

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(II) A mass m on a frictionless surface is attached to aspring with spring constant k as shown in Fig. 14-47. Thismass-spring system is then observed to execute simpleharmonic motion with a period T. The mass m is changedseveral times and the associated period T is measured ineach case, generating the following data Table: (a) Starting with Eq. 14-7b, show why a graph of T2 vs. m isexpected to yield a straight line. How can k be determinedfrom the straight lines slope? What is the lines ^-interceptexpected to be? (b) Using the data in the Table, plot T2 vs. mand show that this graph yields a straight line. Determinethe slope and (nonzero) ^-intercept, (c) Show that anonzero ^-intercept can be expected in our plot theoreticallyif, rather than simply using m for the mass in Eq. 14-7b, weuse m + m0, where m0 is a constant. That is, repeat part (a)using m + ra0 for the mass in Eq. 14-7b. Then use the resultof this analysis to determine k and m0 from your graphsslope and ^-intercept. (d) Offer a physical interpretation form0, a mass that appears to be oscillating in addition to theattached mass m.