Question

A mass of 0.5 kg is attached to a spring of force constant 200 N/m. What is the time period of oscillation?

• A. 0.314 s
• B. 0.50 s
• C. 1.00 s
• D. 2.00 s

Hint:

For a mass-spring system, the time period depends on the mass and the spring constant. The larger the mass, the greater the time period.

Answer 1

The Correct Option is A

Time Period of a Spring-Mass System 

Given:

• Mass, \( m = 0.5\ \text{kg} \)
• Spring constant, \( k = 200\ \text{N/m} \)

Formula:

The time period of oscillation for a mass-spring system is given by: \[ T = 2\pi \sqrt{\frac{m}{k}} \]

Substitution:

\[ T = 2\pi \sqrt{\frac{0.5}{200}} = 2\pi \sqrt{0.0025} = 2\pi \times 0.05 = 0.1\pi \] \[ T \approx 0.1 \times 3.1416 = 0.314\ \text{seconds} \]