Pre-Calc Problem

[jacksonhs]

Couldn't find a pre-calc forum so am posting here.

A spring is attached to the ceiling and pulled 10 cm down from equilibrium and released. The amplitude decreases by 19% each second. The spring oscillates 7 times each second. Find an equation for the distance, D the end of the spring is below equilibrium in terms of seconds, t.

I've done problems like this before but for some reason can't figure this one out.

I will appreciate any help. Thank you.

Jackson

 

[tkhunny]

You have:

Beginning Amplitude
Period of oscillations
Some sense of amplitude deterioration, but it doesn't match up with the Period.

Can you convert (1 - 19%) / (1 second) to an equivalent deterioration that is more consistent with the period of the oscillations? What % per "1/7 second"?

 

[jacksonhs]

You have:

Beginning Amplitude
Period of oscillations
Some sense of amplitude deterioration, but it doesn't match up with the Period.

Can you convert (1 - 19%) / (1 second) to an equivalent deterioration that is more consistent with the period of the oscillations? What % per "1/7 second"?

1/7 expressed in percentage terms is ~14%.

 

[tkhunny]

1/7 expressed in percentage terms is ~14%.

Well, you can't just do 14% 7 times and end up with 19% over the entire 7 pieces of the second. How will you use this information?

Hint: There is a VERY STRONG reason why I wrote "(1 - 19%)" instead of just "19%" in that earlier post.
Hint: Is the reduction of one cycle, when compared to the next cycle, a linear relationship?