Data sheet 51b: Pendulum Harmonic Motion and Hooke's Law Data Table 1: Simple Harmonic Motion Pendulum Diameter of Sphere (m) = 0.02502 Radius of Sphere (m) = 0.01251 Trial String Length Total Pendulum Period of oscillation T2 (Lu) Length 0') {52) (m) (L, = L0 + r) {3) (m) 1 0.159 0.17151 0.80091 0.6414568 2 0.186 0.19851 0.87755 0.7700940 3 0.214 0.22651 0.94059 0.8847095 4 0.240 0.25251 0.99357 0.9871813 5 0.264 0.27651 1.04136 1.084431 6 0.288 0.30051 1 .09009 1 .188296 7 0.32 0.33251 1.14575 1.312743 8 0.348 0.36051 1 . 19557 1 .429388 9 0.384 0.39651 1 .25083 1 .564576 10 0.410 0.42251 1 .29252 1 .677673 Slope of graph T2 vs L1 = _4.079883 542m Gravitational Acceleration \"9\" = _9.676360 W542 % Error = _1.180964% Introduction: This experiment examines Hooke's law and Simple Harmonic Motion. Simple Harmonic Motion (SHM) is when the position of a body can be described as a sinusoidal function of time. This motion is over the same path, which includes an equilibrium position that the simple harmonic oscillator must pass through with each cycle. Examples of SHM include the oscillation of a mass attached to an ideal spring (which will be studied in this experiment), the motion of a simple pendulum (also studied in this experiment) within a grandfather clock, the ticking of a metronome, and many others. SHM occurs whenever the net force or the net torque acting on a body is directly proportional to the displacement of the body from its equilibrium position. An example of such force, which will be studied in this lab, is the restoring force exerted by a stretched or a compressed spring, described by Hooke's law. Another example is the simple pendulum which can be described ideally as a point mass suspended by a massless string from some point about which it is allowed to swing back and forth in a place at a small angle (6