Question

For the oscillations of a spring with spring constant k, the false statement is

• A. Stiff springs have high value of \( k \)
• B. Soft springs have small value of \( k \)
• C. The spring constant is independent of the elastic properties of the spring
• D. For smaller oscillations, the spring executes simple harmonic motion
• E. The period of oscillations of the spring depends upon the value of \( k \)

Hint:

The spring constant \( k \) depends on the material, structure, and dimensions of the spring. It is not independent of these factors.

Answer 1

The Correct Option is C

- Option A: Stiff springs have a high value of spring constant \( k \), which represents the stiffness of the spring. This statement is correct. - Option B: Soft springs have a low value of spring constant \( k \), which indicates a less stiff spring. This statement is correct. - Option C: The spring constant \( k \) is actually dependent on the material's elasticity and the dimensions of the spring. A spring with a different material or structure will have a different spring constant, so this statement is false. - Option D: For small oscillations, the spring follows simple harmonic motion (SHM) where the restoring force is directly proportional to the displacement. This statement is correct. - Option E: The period of oscillations of a spring is given by \( T = 2\pi \sqrt{\frac{m}{k}} \), so the period depends on the value of \( k \). This statement is correct. Thus, the false statement is (C), as the spring constant is indeed dependent on the elastic properties of the spring.