Oscillations of Spring with Viscous Medium

[robax25]

Homework Statement

A spring with K=12N/m and an attached bob oscillates in a viscous medium.Amplitude is 6cm from equilibrium position at 1.5 s and Next amplitude of 5.6 cm occurs at 2.5s. what is its displacement at 3s and 4.5s and t=0s

Homework Equations

x(t)=Xme^-bt/2m

The Attempt at a Solution

x=4.16cm
[/B]

 

[scottdave]

Where is the oscillating portion of your x(t) expression?

 

[robax25]

e=0.133 as the ration of decay.

x(t)=xm x .133 and However, I am confused to find Xm(amplitude at 3 s) . I considered Xm=5.2cm at 3s. But, it is a false assumption.

 

[haruspex]

e=0.133 as the ration of decay.

x(t)=xm x .133 and However, I am confused to find Xm(amplitude at 3 s) . I considered Xm=5.2cm at 3s. But, it is a false assumption.

That is not what scottdave asked. The x(t) expression should have a trigonometric factor to represent the oscillation.

 

[robax25]

I do not get it. How can I calculate trigonometric factor?

 

[haruspex]

I do not get it. How can I calculate trigonometric factor?

You know the period. What is the general formula for a damped oscillation?

 

[scottdave]

I do not get it. How can I calculate trigonometric factor?

Try looking here to see if this helps. http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html

David Scott
Kwik Kopy Printing
1010 Spring Cypress Road
Spring, Texas 77373
281.353.797

 

[scottdave]

I do not get it. How can I calculate trigonometric factor?

Try looking here to see if this helps. http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html

David Scott
Kwik Kopy Printing
1010 Spring Cypress Road
Spring, Texas 77373
281.353.797

 

[robax25]

You know the period. What is the general formula for a damped oscillation?

x(t)=Xme^-bt/2m here Xm is amplitude, b is damping factor

 

[scottdave]

x(t)=Xme^-bt/2m here Xm is amplitude, b is damping factor

So is Xm the amplitude of the cosine wave? Did you look at the hyperphysics link I sent?

 

[robax25]

I saw it ..they consider a for amplitude.However, I consider Xm

 

[Nathanael]

The Attempt at a Solution

x=4.16cm[/B]

“The attempt at a solution” means your steps and thoughts. Please show effort.

 

[haruspex]

x(t)=Xme^-bt/2m here Xm is amplitude, b is damping factor

But clearly that does not produce an oscillation - unless that X_m is also a function of time.
What is the formula for an undamped SHM?

 

[robax25]

Undamped SHM x(t)=Xmcos(ωt+∅)

 

[robax25]

for damped Oscillation x(t)=A e^-bt/2m cos(ωt+Φ). I did not notice it properly

Here A is amplitude

 

[haruspex]

for damped Oscillation x(t)=A e^-bt/2m cos(ωt+Φ). I did not notice it properly

Here A is amplitude

Right.
Now it is a matter of plugging the known facts into that equation to determine A, b/m, ω and φ.
So you need four equations. Knowing the displacement at a given time gives you one, and knowing that this is a local extrememum gives you another. You have that for two different times, giving you four equations altogether.

 

[robax25]

how can I get the position at 3s?

 

[haruspex]

how can I get the position at 3s?

Once you have determined the four constants as I described in post #16, you plug t=3 into your equation in post #15.