# Damping problem

## 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

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

## The Attempt at a Solution

x=4.16cm
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scottdave
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Where is the oscillating portion of your x(t) expression?

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.

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haruspex
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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.

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

haruspex
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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
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scottdave
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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
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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?

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

Nathanael
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## The Attempt at a Solution

x=4.16cm[/B]
“The attempt at a solution” means your steps and thoughts. Please show effort.

haruspex
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x(t)=Xme^-bt/2m here Xm is amplitude, b is damping factor
But clearly that does not produce an oscillation - unless that Xm is also a function of time.
What is the formula for an undamped SHM?

Undamped SHM x(t)=Xmcos(ωt+∅)

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

Here A is amplitude

haruspex
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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.

how can I get the position at 3s?

haruspex