Question

A spring produces extension \({}'x'\) by applying a force \({}'F'\) N. A body of mass \({}'m'\) suspended from spring oscillates vertically with period \({}'T'\). The mass of the suspended body is (Neglect mass of spring)

• A. \(\frac{T^{2}F}{4\pi ^{2}x}\)
• B. \(\frac{TF}{4\pi x}\)
• C. \(\frac{TF^{2}}{4\pi ^{2}x}\)
• D. \(\frac{T^{2}F}{4\pi x}\)

Hint:

Get the spring constant from F over x and substitute it into the spring-mass time period formula.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
The spring constant is \(k=\frac{F}{x}\).

Step 2: Time period
A mass \(m\) on the spring oscillates with \(T=2\pi\sqrt{\frac{m}{k}}\).

Step 3: Calculation
Squaring, \(T^{2}=4\pi^{2}\frac{m}{k}\), so \(m=\frac{T^{2}k}{4\pi^{2}}\).
Substitute \(k=\frac{F}{x}\):
\(m=\frac{T^{2}F}{4\pi^{2}x}\)

Step 4: Compare the options
This is option (A).

Final Answer:
The mass is T squared F divided by 4 pi squared x. \[ \boxed{\text{(A) }\dfrac{T^{2}F}{4\pi^{2}x}} \]