Question

In an experiment to determine the period of oscillation of a loaded spiral spring, T2 was plotted on the vertical axis and M on the horizontal axis. T is the period while M is the effective mass. Which of the following is CORRECT?

A. the slope of the graph gives the acceleration due to gravity, g
B. the inverse of the slope of the graph gives M
C. the intercept on the vertical axis of the graph gives M
D. the intercept on the horizontal axis of the graph gives M

Answer 1

Answer on Question #55610, Physics / Mechanics | Relativity

In an experiment to determine the period of oscillation of a loaded spiral spring, $T^2$ was plotted on the vertical axis and $M$ on the horizontal axis. $T$ is the period while $M$ is the effective mass. Which of the following is CORRECT?

A. the slope of the graph gives the acceleration due to gravity, g

B. the inverse of the slope of the graph gives M

C. the intercept on the vertical axis of the graph gives M

D. the intercept on the horizontal axis of the graph gives M

Solution:

There is a relationship between the period of oscillation $T$ , the loaded mass $M$ and the effective mass of the spiral spring $m$ .

$$T = 2 \pi \sqrt {\frac {M + m}{k}}$$

where, $k$ is the spring constant.

We then reduce the expression to a linear one by squaring both sides of the equation.

$$T ^ {2} = 4 \pi^ {2} \frac {M + m}{k}$$ $$T ^ {2} = 4 \pi^ {2} \frac {M}{k} + 4 \pi^ {2} \frac {m}{k}$$

By plotting the values of $T^2$ against the corresponding values of $M$ , we would obtain a straight line graph which does not pass through the origin as shown in figure.

The intercept on the horizontal axis is obtained when $T^2 = 0$ .

$$M = - m$$

which gives us the effective mass of the spiral spring.

Answer: D. the intercept on the horizontal axis of the graph gives M

http://www.AssignmentExpert.com/