Forced oscillation (mass & spring)

[kash25]

Homework Statement

A 2 kg object attached to a spring moves without friction and is driven by an external force given by F = (3.00N)sin(2$$\pi$$t). The force constant of the spring is 20.0N/m.
Find the amplitude of the motion.

Homework Equations

I am not sure but I am trying to use:
A = (F₀/m)/[tex]\sqrt{}(w^2-w₀^2)^2[/tex]

The Attempt at a Solution

Applying this equation using w equals 2pi and w₀ is k/m (10) gives an amplitude of 0.00173. The solution in the book says 5.09cm.
Am I approaching this question correctly?

 

[alphysicist]

Hi kash25,

Homework Statement

A 2 kg object attached to a spring moves without friction and is driven by an external force given by F = (3.00N)sin(2$$\pi$$t). The force constant of the spring is 20.0N/m.
Find the amplitude of the motion.

Homework Equations

I am not sure but I am trying to use:
A = (F₀/m)/[tex]\sqrt{}(w^2-w₀^2)^2[/tex]

The Attempt at a Solution

Applying this equation using w equals 2pi and w₀ is k/m (10)

w₀ is not equal to k/m. If you correct this you should get the right answer.

 

[Gear300]

Not exactly sure...but that equation you have might be for forced oscillations working against friction; in this case there is no friction.

 

[alphysicist]

Not exactly sure...but that equation you have might be for forced oscillations working against friction; in this case there is no friction.

No, it's the right equation. If it was a damped spring there would be another term under the radical. Using that equation (with the corrected value for w₀) gives the answer given in the post.

 

[Quachama]

remember that w0 = sqrt (k/m).

That will give you the right answer :)

 

[kash25]

stupid mistake..thanks for your help!