Question

The time period of oscillations of a spring of force constant 65 N m^-1 with its upper end fixed to a rigid support and carrying a mass of 650 g at its lower end is:

• A. 314 ms
• B. 628 ms
• C. 157 ms
• D. 785 ms

Hint:

For spring-mass systems, the time period depends only on mass and spring constant, not on amplitude or gravity. Convert units carefully: 1 s = 1000 ms.

Answer 1

The Correct Option is B

The time period of a spring-mass system is given by $T = 2\pi \sqrt{\frac{m}{k}}$, where $m$ is the mass and $k$ is the spring constant.
Given: $k = 65$ N m$^{-1}$, $m = 650$ g = 0.65 kg.
So, $T = 2\pi \sqrt{\frac{0.65}{65}} = 2\pi \sqrt{0.01} = 2\pi \times 0.1 = 0.2\pi$ seconds.
Using $\pi \approx 3.14$, $T \approx 0.2 \times 3.14 = 0.628$ s = 628 ms.