# Proof of oscillation about the equilibrium

Bonnie

## Homework Statement

The problem is question 2(a) in the attached pdf. I seem to find myself at a dead end and am not sure where to go from here - I will attach my working in a separate file, but basically I need to show that the oscillator passes/crosses over the x = 0 boundary at a positive time, but I don't seem to be able to do that (or have enough information to) without ending up with nothing, or an impossible equation, like an exponential term = 0.

## The Attempt at a Solution

#### Attachments

• PHYS205 Assignment 8.pdf
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• 20180514_101513.jpg
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## Answers and Replies

Homework Helper
Your picture is half illegible. Seems you do find an ##\omega## though.
However: your try with an intial displacement of 0 of course doesn't let the thing oscillate !

free tip: work with symbols, not with numbers. Only at the last moment, if/when a value is needed, subtitute values.

Bonnie
Your picture is half illegible. Seems you do find an ##\omega## though.
However: your try with an intial displacement of 0 of course doesn't let the thing oscillate !

free tip: work with symbols, not with numbers. Only at the last moment, if/when a value is needed, subtitute values.

ω is 20 rads-1, from the equation (I have shown it only with values substituted):
p = -γ/2 +/- √[ω2 - (γ/2)2]
where ω2 = 400 and γ = 5\

And I set x(0) = D, not 0, as x is a function of t, is that incorrect?
Thanks

Homework Helper
And I set x(0) = D, not 0, as x is a function of t, is that incorrect?
No, that's correct. But it looks a lot like a zero on my screen.

has ##x=Ce^{-{5\over 2}t} e^{\rm illegible}## when originally it was
( so probably ##x=Ce^{pt} ## ?) and you found two ##p##. What happened to the second ?

#### Attachments

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Bonnie
No, that's correct. But it looks a lot like a zero on my screen.

Your Solution View attachment 225681
has ##x=Ce^{-{5\over 2}t} e^{\rm illegible}## when originally it was View attachment 225682 ( so probably ##x=Ce^{pt} ## ?) and you found two ##p##. What happened to the second ?
I'll try to attach a better photo, but the second p is included in the e+/- 393.75j

#### Attachments

• 20180514_101513.jpg
25.7 KB · Views: 385
Bonnie
I'll try to attach a better photo, but the second p is included in the e+/- 393.75j
Ah, I've just realized that the photo quality is significantly decreased by uploading it here. Apologies for that