30-Nov-2016: Mass-Spring Oscillations Lab

Apparatus: A mass, several spring, a motion detector.

Model: 

Process: We have 5 different spring, so we divided into five group. Each group use one spring to collect data. For Kinetic energy purposes one-third of the spring's mass contributes to the KE of the mass-spring system. This is also true as far as contributing to the oscillating mass in the system when you go to determine the period. The effective mass of the spring is (1/3)mspring.
    Therefore, we get:
                              Oscillating mass=hanging mass + hook mass(3.7 g) + (1/3)mass of spring
    First, we are going to find the spring constant of our spring. We hang the spring, and we measure the distance from the end of the spring to the ground, d1=0.37 cm. Then, we hang a 100g weight on the spring and measure the distance from the end of the spring to the ground, d2=0.52 cm. By using:

                                                                     F=Δxk
                                                                     Δx=d2-d1
                                                                     k=6.53 N/m

    Now, we want to let the oscillating mass be 115g and find out the period. We measure the mass of the spring with the hook on it. Mspring+hook=11.3g. By calculation:

                                               Mspring=Mspring+hook-Mhook=7.6 g
                                               Mhang=Moscillating-(1/3)Mspring-Mhook=115-2.533-3.7=109g

    We set the apparatus by hanging the spring and place the motion detector right below the spring. We hang 109 g mass on the spring, pull down the spring a little bit, release it, and start collect the data.

    We get the period from the graph:
                                                              T=0.735 s

    By sharing the data between the group, we get:

    We plug in these number into the LoggerPro. Basing on the equation:

    We try to linear fit by equation: T=Ak^-0.5, we get:

    From the graph, the constant of the equation A=2.111. In theory, 

                                                        The theoretical A=2.1307
                                                        The experimental A=2.111
                                                        1% off

    Now, we use our spring and collect different period hanging different mass. We get:

    We use Mhang+(1/3)Mspring+Mhook=Moscillating to find out the actual oscillating mass. We plug these data into the LoggerPro. Basing on the equation:

    We try to linear fit by equation: T=Am^0.5, we get:

     From the graph, the constant of the equation A=2.478. In theory, 

                                                            The theoretical A=2.4588
                                                            The experimental A=2.478
                                                            1% off