Pfautz+Lab+17


 * Spring with mass**

__Procedure:__ Part 1: 1) Hang the spring from the ring stand and attach the mass to the bottom of the spring. 2) Pull the spring to amplitude 2cm. 3) Conduct the procedure starting with a mass of 50g and increasing it by intervals of 5g each trial for five trials. 4) Record the periods for each mass.

Part 2: 1) Hang the spring from the ring stand and attach the mass to the bottom of the spring. 2) Pull the spring to amplitude 2cm. 3) Repeat the process but increase the amplitude by increments of 2cm per trial for five trials. 4) Record the periods for each amplitude.

 Data: Table 1
 * Change in Period Due to Change in Mass ||
 * Trial || Mass (g) || Cycles || Time || Period (s/cycle) ||
 * **1 ** || 50 || 10 || 5.87 || 0.59 ||
 * 2 || 55 || 10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">5.50 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.55 ||
 * <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">3 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">60 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">6.32 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.63 ||
 * <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">4 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">65 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">7.00 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.70 ||
 * <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">5 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">70 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">7.38 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.74 ||

<span style="font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">Table 2
 * <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">Change in Period Due to Change in Amplitude ||
 * <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">Trial || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">Amplitude (cm) || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">Cycles || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">Time || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">Period (s/cycle) ||
 * <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">1 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">2 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">6.20 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.62 ||
 * <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">2 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">4 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">5.95 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.60 ||
 * <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">3 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">6 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">6.04 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.60 ||
 * <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">4 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">8 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">5.96 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">0.60 ||
 * <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">5 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: right;">10 || <span style="color: #000000; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px;">n/a || <span style="color: #000000; display: block; font-family: 'Trebuchet MS','sans-serif'; font-size: 16px; text-align: center;">n/a ||

__Analysis__



The graphs show that increasing the mass increases the period and the slope in the second graph shows that changing the amplitude does not affect the period. The change in period due to change in mass has a positive linear correlation. These correlate with the equation T = 2π(m/k)^(1/2). Changing the amplitude doesn’t affect the period since is not in the equation.