T= 2π√m+m\k where m = effective mass of the spring and k =spring constant, show how the values of m and k can be determined from graph.

Answer 1

To determine the values of m and k from a graph, we would plot the period (T) of the oscillation against the square root of the effective mass (m). Then, we would find the slope of the tangent at each point of the graph and use it to calculate the values of m and k.

Step 1: Plot the graph of T vs. √m
On the graph, plot the period (T) of the oscillation on the y-axis and the square root of the effective mass (m) on the x-axis. You should have a set of points on the graph that represent different periods and masses.

Step 2: Find the slope of the tangent at each point of the graph
The slope of the tangent at each point on the graph represents the proportionality constant between T and √m. In other words, the slope of the tangent is equal to 2π divided by the square root of the spring constant k. So,

Slope of the tangent at each point = 2π/√k

Step 3: Calculate the value of k
To find the value of k, rearrange the above equation:

k = (2π/Slope)^2

Use the slope value from Step 2 to calculate the value of k.

Step 4: Calculate the value of m
We can also find the effective mass m of the spring by rearranging the initial equation for m:

m = (T^2 * k) / (4π^2)

Use values for T and k from the previous steps and calculate the value of m.

In summary, the values of the effective mass m and the spring constant k can be determined from a graph by plotting the period (T) versus the square root of the effective mass (m), finding the slope of the tangent at each point of the graph, and then calculating m and k using the equations above.