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Which of the following is/are the characteristics of simple harmonic motion (i) The total energy is conserved (ii) The acceleration is directly proportional to the displacement and is directed towards its mean position (iii) The simple harmonic motion cannot be represented using sinusoidal functions (iv) There are a maximum and minimum displacement about the equilibrium point

Which of the following is/are the characteristics of simple harmonic motion (i) The total energy is conserved (ii) The acceleration is directly proportional to the displacement and is directed towards its mean position (iii) The simple harmonic motion cannot be represented using sinusoidal functions (iv) There are a maximum and minimum displacement about the equilibrium point Correct Answer (i), (ii) & (iv)

CONCEPT:

  • Simple harmonic motion is a kind of oscillatory motion in which the particle gets displaced equally into both sides of the equilibrium point under restoring force.
  • The restoring force is always directed towards the equilibrium point.
  • The equation of motion of simple harmonic motion is given by

⇒ Y = A Sin(kx + ωt + ϕ )

Where A = Amplitude,K = Wave vector,ω = Angular velocity, ϕ = Phase

EXPLANATION:

  • Simple harmonic motion is a kind of oscillatory motion in which the particle gets displaced equally into both sides of the equilibrium point under restoring force.
  • The table below gives the characteristics of simple harmonic motion

Characteristics of simple harmonic motion

SHM is regularly repeating. i.e., SHM is periodic in nature

The acceleration is directly proportional to the displacement and is directed towards the mean position

The total energy is conserved in a simple harmonic motion

SHM can be represented using periodic functions like sine or cosine functions
  • From inspecting the table it is clear statements (i), (ii) & (iv) are correct. Hence option 3 is the answer
  • The simple harmonic motion can be represented using any periodic functions like sine or cosine. Hence statement (iii) is incorrect

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