Physics

Problem

FORCE CONSTANT (1996M1) A thin, flexible metal plate attached at one end to a platform, as shown above, can be used to measure mass. When the free end of the plate is pulled down and released, it vibrates in simple harmonic motion with a period that depends on the mass attached to the plate. To calibrate the force constant, objects of known mass are attached to the plate and the plate is vibrated, obtaining the data shown. a. The data obtained in the experiment is shown in the table. Calculate the period.

Mass $(\mathrm{kg})$	$t_{\text {avg }}$ for 10 vibrations $(\mathrm{s})$	$T(\mathrm{~s})$
0.10	8.86
0.20	10.6
0.30	13.5
0.40	14.7
0.50	17.7

b. Complete the last column in the table by calculating the quantity that needs to be graphed to provide a linear relationship from the data collected. c. Sketch a graph of the best straight-line fit to the data points. d. From your graph clearly calculate the force constant of the metal plate. ![](https://storage.googleapis.com/diraq-contents/question-bank/question-images/5638a8b14b31/2025_11_20_b9b74b2df578ad89a22fg-4.jpg)

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