Question

Which of these forces could result in simple harmonic motion? The positive values of F(x) correspond to the forces acting in the positive x direction. Select all that applyA. F(x)=−9(x−6)1/2B. F(x)=9x1/2C. F(x)=−9x1/2D. F(x)=9xE. F(x)=−9xF. F(x)=−9x+6

Answer 1

Answer:

E.F(x )= - 9 x

F.F(x )= - 9 x + 6

Explanation:

    Given that

$F(x)=-9(x-6)^{\frac{1}{2}}$

$F(x)=9x^{\frac{1}{2}}$

$F(x)=-9x^{\frac{1}{2}}$

F(x )=  9 x

F(x )= - 9 x

F(x )= - 9 x + 6

We know that ,for simple harmonic motion

F= - k x

k=constant

The power of x should be one.We can say that it is linear equation between force and displacement x.The force is proportional to the displacement but in the opposite direction.

Therefore the following forces shows the harmonic motion.

F(x )= - 9 x

F(x )= - 9 x + 6

Answer 2

Harmonic motion is the oscillating motion. Options D and E are correct.

$E.F(x )= - 9 x\\\it F.F(x )= -9x + 6$

Simple Harmonic motion:

• It motion in which an oscillating body experiences a force,  proportional to the ​displacement, on restoration but in opposite directions.

• It follows Hooke's law which states that the force is directly proportional to its compression of spring.
• For example- Bouncing on spring and vibration of a guitar string.

From Hooke's Law,

$F = kx$

Where,

$k$- Spring constant

$x$ - displacement

Therefore, option D and E shows the simple harmonic motion.

Learn more about Simple Harmonic motion:

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