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Solve this problem Which one of the following equations of motion represents simple harmonic motion?

Which one of the following equations of motion represents simple harmonic motion?

  • Option 1)

    Acceleration = -k(x +a) 

  • Option 2)

    Acceleration = k(x + a)

  • Option 3)

    Acceleration = kx

  • Option 4)

    Acceleration = -k0x + k1x2

    where k, k0, k1 and a are all positive.

 
Answers (1)
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Equation of S.H.M. -

a=-frac{d^{2}x}{dt^{2}}= -w^{2}x

w= sqrt{frac{k}{m}}

 

- wherein

x= Asin left ( wt+delta 
ight )

 

 a=-Kx

where x=x+a\\ a=-K(x+a)

In S.H.M acceleration is directly proportional to the displacement from the mean position 

Also the acceleration is in the opposite direction of displacement 


Option 1)

Acceleration = -k(x +a) 

This solution is correct 

Option 2)

Acceleration = k(x + a)

This solution is incorrect 

Option 3)

Acceleration = kx

This solution is incorrect 

Option 4)

Acceleration = -k0x + k1x2

where k, k0, k1 and a are all positive.

This solution is incorrect 

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