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Consider the case of a student wishing to determine the spring constant for a spring by measuring the period of oscillation of a mass on the spring. The student knows that the relationship between the spring constant (k), the mass (m), and the period of oscillation (T) is given by the equation T = 2πsquare root of m/k. (1) This is not a Iinear equation; to see this, plot the period (T) vs. mass ( m). E quation ( 1) can be made linear by squaring both sides of equation (1). Next try to put the equation into y = mx +b form (dont confuse m for slope in this equation with m for mass in equation 1 above). T2, is the independent variable, like y, m is the independent variable. Now plot T 2 versus m and find the slope of the Iine in your graph. The slope of the resulting Iine can be used to determine the spring constant k. Show your calculation of the slope and k, the spring constant on your graph.

Consider the case of a student wishing to determine the spring constant for a spring by measuring the period of oscillation of a mass on the spring. The student knows that the relationship between the spring constant (k), the mass (m), and the period of oscillation (T) is given by the equation T = 2πsquare root of m/k. (1) This is not a Iinear equation; to see this, plot the period (T) vs. mass ( m). E quation ( 1) can be made linear by squaring both sides of equation (1). Next try to put the equation into y = mx +b form (dont confuse m for slope in this equation with m for mass in equation 1 above). T2, is the independent variable, like y, m is the independent variable. Now plot T 2 versus m and find the slope of the Iine in your graph. The slope of the resulting Iine can be used to determine the spring constant k. Show your calculation of the slope and k, the spring constant on your graph.

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Consider the case of a student wishing to determine the spring constant for a spring by measuring the period of oscillation of a mass on the spring. The student knows that the relationship between the spring constant (k), the mass (m), and the period of oscillation (T) is given by the equation T = 2πsquare root of m/k. (1)

This is not a Iinear equation; to see this, plot the period (T) vs. mass ( m). E quation ( 1) can be made linear by squaring both sides of equation (1). Next try to put the equation into y = mx +b form (dont confuse m for slope in this equation with m for mass in equation 1 above). T2, is the independent variable, like y, m is the independent variable. Now plot T
2 versus m and find the slope of the Iine in your graph. The slope of the resulting Iine can be used to determine the spring constant k. Show your calculation of the slope and k, the spring constant on your graph.

Next, consider the case of a student wishing to determine the spring constant for a spring by measuring the period of oscillation of a mass on the spring. The student knows that the relationship between the spring constant (k), the mass (m), and the period of oscillation (T) is given by the equation T = 2n, k (1) This is not a linear equation; to see this, plot the period (T) vs. mass (m). Equation (1) can be made linear by squaring both sides of equation (1). Next, try to put the equation into y = mx +b form (don't cofuse m for slope in this equation with m for mass in equation 1 above). T2 is the dependent variable like y, mis the independent variable, like x. Now plot T2 versus m and find the slope of the line in your graph. The slope of the resulting line can be used to determine the spring constant, k. Show your calculation of the slope and k, the spring constant, on your graph. Mass 0.025 0.05 0.100 0.15 0.200 0.250 0.3 (kg) T (S) T²(s') 0.379 0.530 0.750 0.920 1.100 1.200 1.300
Transcribed Image Text:Next, consider the case of a student wishing to determine the spring constant for a spring by measuring the period of oscillation of a mass on the spring. The student knows that the relationship between the spring constant (k), the mass (m), and the period of oscillation (T) is given by the equation T = 2n, k (1) This is not a linear equation; to see this, plot the period (T) vs. mass (m). Equation (1) can be made linear by squaring both sides of equation (1). Next, try to put the equation into y = mx +b form (don't cofuse m for slope in this equation with m for mass in equation 1 above). T2 is the dependent variable like y, mis the independent variable, like x. Now plot T2 versus m and find the slope of the line in your graph. The slope of the resulting line can be used to determine the spring constant, k. Show your calculation of the slope and k, the spring constant, on your graph. Mass 0.025 0.05 0.100 0.15 0.200 0.250 0.3 (kg) T (S) T²(s') 0.379 0.530 0.750 0.920 1.100 1.200 1.300
Expert Solution
Step 1

Given:

  M                          T2

0.025                      0.144

0.05                        0.281

0.1                          0.562

0.15                         0.846

0.2                           1.21

0.25                         1.44

0.3                           1.69

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