A spring-mass system consisting of several masses and a spring was set up Differ

Question

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.

Explanation / Answer

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

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.