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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

Answer: C

The false statement is The spring constant is independent of the elastic properties of the spring.

The spring constant is a measure of the spring's stiffness, and it depends directly on the elastic properties (the material's modulus) and on the spring's dimensions. So this statement is false.

The others are true: stiff springs have large k and soft springs small k; for small oscillations the restoring force is proportional to displacement, giving SHM; and the period \(T = 2\pi\sqrt{\frac{m}{k}}\) depends on k.

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