Simple harmonic motion -- The spring and mass are immersed in a fluid....

[Asel]

1.
A mass, M = 1.61 kg, is attached to a wall by a spring with k = 559 N/m. The mass slides on a frictionless floor. The spring and mass are immersed in a fluid with a damping constant of 6.33 kg/s. A horizontal force, F(t) = Fd cos (ωdt), where Fd = 52.5 N, is applied to the mass through a knob, causing the mass to oscillate back and forth. Neglect the mass of the spring and of the knob and rod.

a) At approximately what frequency will the amplitude of the mass' oscillation be greatest?

b) What is the maximum amplitude?

c) If the driving frequency is reduced slightly (but the driving amplitude remains the same), at what frequency will the amplitude of the mass' oscillation be half of the maximum amplitude?2. I have used the equation of damped oscillations:
Wd^2=(k/m-b^2/4m^2)
A=Fmax/((k-mWd^2)^2+(bWd)^2)
For shm,
X=Acos(wt+Φ)

The Attempt at a Solution

I used the first equation and found the first question as 18.537hz but the answer is not correct. The second question will be found by the use of the second equation so i couldn't solve this too. And i did not understand the last question. Can somebody help me please about this?

Thanks for any help help provided.
I am new here so if i have any mistake sorry about that!:)

 

[scottdave]

I found ω_d = 18.53 radians/sec. What you now need to do is know that ω = 2πf, so f = ω/(2π)

 

[ehild]

2. I have used the equation of damped oscillations:
Wd^2=(k/m-b^2/4m^2)
A=Fmax/((k-mWd^2)^2+(bWd)^2)

The Attempt at a Solution

I used the first equation and found the first question as 18.537hz but the answer is not correct. The second question will be found by the use of the second equation so i couldn't solve this too.

The equation for A (in red) is not correct. The amplitude depends on the driving frequency, ω_d and you miss a square root.

 

[scottdave]

The PDF in this link may help you understand this. http://academics.hamilton.edu/physics/smajor/Courses/195Guides/L4_Resonance.pdf

 

[Asel]

I found ω_d = 18.53 radians/sec. What you now need to do is know that ω = 2πf, so f = ω/(2π)

Thank you!

 

[Asel]

The equation for A (in red) is not correct. The amplitude depends on the driving frequency, ω_d and you miss a square root.

Okay. Thank you!