Part II Simple Harmonic Motion (Mass on a Spring) mm; In this experiment, the you can observe and study the periodic motion in a plane and investigate the relation between the periodic time of a mass on a spring and the hanged mass. The you can determine the spring constant of the spring using the experimental data of this experiment. Thgg; A common example of an object oscillating back and forth under the effect of a restoring force that is directly proportional to the displacement from equilibrium (Hooke's Law) is the case of a mass on the end of an ideal spring. Hooke's Law Is the name that was given to this relationship between force and displacement of a mass undergoes an oscillatory motion. kX .................. (5) Here, F is the restoring force, x is the displacement from equilibrium, and k is the spring constant. Remember that the minus sign indicates the restoring force is in the direction opposite to the displacement. Mass on a Spring The motion of a mass on a spring can be described as Simple Harmonic Motion (SI-1M) as shown in Fig 2, where the net force can be described by Hooke's law. We can now determine how to calculate the periodic time and frequency of an oscillating mass (m). Newton's second law gives the equation of motion: - dzx _ k mgkx=ma=m2 .................. (6) '9' Z dt ._ The solution of this equation is: it I -kx x = Asin(a)t) .................. (7) l mg Where, to is the angular velocity of the oscillatory motion and is given by: HOOK\" LEW: spring a) = .................. (s) . m Fig. 2 Then the periodic time of oscillation is given by T=2:n:/o) m then, T = 27.:1 / ? .................. (9) Where T: is the periodic time, m: is the mass hanged on the spring and k: is the spring constant. To satisfy the objectives of this experiment, follow the link below and do the following steps. 4 https:l/phet.colorado.edu/sims/html/massesandsprings/latest/masses-and-springs en.htm1 1. 3. Click on E) screen and use the mass controller to control the mass hanged H= 'l' y to the spring (m), set no =150kg. mag, / \\ 59\" Record the mass in table 2. Control the spring constant using the spring constant controller and set it at the !a_rge value. Click on m meter and drag it near the spring. Put \\/ on period trace selection to trace the line of ill cycle. Compress the spring to the maximum compression, Set the simulation speed at slow mode. Press on start Bolton, watch the trace of El cycle, then press the arrowhead on mt meter to start measuring the periodic time (T). Record the periodic time in table 2. Repeat the previous steps for different masses of (m) as shown in the table 2. Record your data in the table 2. Data Analysis; 5. Calculate the square of the periodic time (T2). 6. Use Excel Wm plot a graph of T2 versus m, T2 as the ordinate El m as the abscissa. 7. Use the equation of the graph to determine its slope, use the slope of the line to calculate the acceleration due to gravity g which is given by: 4 1:2 k = Ta 1 2 slope 50 100 140 180 220 260 300 Questions: 1. Explain what will happen to the periodic time? if you change the spring constant to the low value. 2. Explain theoretically how can you determine the spring constant using hooks law