A springmass system consisting of several masses and a sprin

A spring-mass system consisting of several masses and a spring was set up Different values or the period and the mass were recorded. A plot of T^2 vs. m is given in the figure below. The equation governing the period T^2 = The fitted mathematical equation for the data is y = Bx. Use this relationship to answer the following questions. What is the value of B (with units) in the fitted equation? Write a few sentences to explain how you can find spring constant, k, from the fitted equation. Determine the value of the spring constant.

Solution

We know that the time period of motion for a spring mass system is given as T = 2(m/k)

Squaring the above relation, we get: T² = 4²m/k which is the form given in the question.

Clearly, if we plot T² against m, we will get a straight line with slope equal to 4²/k [Compare it with the form y = Bx where B is the slope of the line]

Part 3.) Now from the graph we can find the slope of the given line which would be same as the value for B.

Hence B = (0.8 - 0.4) / (0.2 - 0.1) = 4 is the required value.

Part 4.) Now, from the fitted equation we can say that B is same as 4²/k. Also, we know that value for B from the graph, hence we can equate the above two and then resolve to find the required value for K.

Part 5.) Equating B with 4²/k,. we get:

4²/k = 4

or. k = ²

or, k = 9.8596 N /m

Therefore the required spring constant is 9.8596 N /m