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

• Asel
In summary, the conversation discusses a mass attached to a wall by a spring, immersed in a fluid with a damping constant. A horizontal force is applied causing the mass to oscillate. The questions focus on the frequency and amplitude of the oscillation, and how they are affected by the driving frequency. The first equation used is incorrect, but the correct equation can be found in the provided link.
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!:)

Last edited by a moderator:
I found ωd = 18.53 radians/sec. What you now need to do is know that ω = 2πf, so f = ω/(2π)

Asel
Asel said:
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, ωd and you miss a square root.

Asel
scottdave said:
I found ωd = 18.53 radians/sec. What you now need to do is know that ω = 2πf, so f = ω/(2π)
Thank you!

ehild said:
The equation for A (in red) is not correct. The amplitude depends on the driving frequency, ωd and you miss a square root.
Okay. Thank you!

## 1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which the restoring force is directly proportional to the displacement from equilibrium and is always directed towards the equilibrium point.

## 2. How does a spring and mass immersed in a fluid exhibit simple harmonic motion?

When a spring and mass are immersed in a fluid, the fluid creates a damping force that opposes the motion of the mass. This results in the mass oscillating back and forth around the equilibrium point, exhibiting simple harmonic motion.

## 3. What factors affect the frequency of simple harmonic motion in this system?

The frequency of simple harmonic motion in a spring and mass system immersed in a fluid is affected by the mass of the object, the stiffness of the spring, and the damping coefficient of the fluid.

## 4. How is the amplitude of simple harmonic motion affected by the presence of a fluid?

The amplitude of simple harmonic motion in a system with a fluid is decreased due to the damping force exerted by the fluid. This means that the oscillations of the mass will become smaller and eventually come to a stop due to the dissipation of energy through the fluid.

## 5. Can simple harmonic motion in a fluid be used in real-world applications?

Yes, simple harmonic motion in a fluid is commonly seen in real-world applications such as in the suspension of vehicles, shock absorbers, and pendulum clocks. It is also used in the study of fluid dynamics and in the design of buildings to withstand earthquakes.

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