Basic SHM 2

Classical Mechanics Level 2

Which equation is known as the Hallmark of SHM?

  1. d 2 x d t 2 + x ω 2 = 0 \dfrac{d^2 x}{dt^2} + x\omega^2 = 0 .

  2. a ( t ) = − ω 2 A sin ⁡ ( ω t + ϕ ) a(t) = -\omega^2 A \sin(\omega t + \phi) .

  3. v 2 ω 2 A 2 + x 2 A 2 = 1 \dfrac{v^2}{\omega^2 A^2} + \dfrac{x^2}{A^2} = 1 .

  4. x = A sin ⁡ ( ω t ) + ϕ x = A \sin(\omega t) + \phi .

3 1 2 4

Harshi Singh by Harshi Singh , 20, India

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1 solution

Anandhu Raj
Feb 2, 2016

For an SHM,

a = − ω 2 x a=-\omega ^{ 2 }x

⇒ d 2 x d t 2 = − ω 2 x \Rightarrow \frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } =-\omega ^{ 2 }x

⇒ d 2 x d t 2 + ω 2 x = 0 \boxed{\Rightarrow \frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +\omega ^{ 2 }x=0}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

yes correct

Ashish Menon - 5 years, 4 months ago

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