Posted by **Sarah** on Monday, June 9, 2014 at 12:16am.

A weight attached to a long spring is bouncing up and down. As it bounces, its distance from the floor varies periodically with time. You start a stopwatch. When the stopwatch reads 0.3 seconds, the weight reaches its first high point 65 cm above the ground. The next low point, 25 cm above the ground, occurs at 1.8 seconds. What are the next two times the spring is at a high of 50 cm after 2.0 seconds?

- trig -
**Reiny**, Monday, June 9, 2014 at 9:00am
let's fit the data to a curve of the type

f(t) = a cos k(t +d) + c

from highest to lowest = 65-25= 40 cm

so a = 20

from highest to lowest = .3 s to 1.8 s

so period = 3 seconds

2π/k = 3

k = 2π/3

so far we have

f(t) = 20 cos (2π/3) (t +d) + c

let's raise the curve 45 cm

f(t) = 20 cos (2π/3) (t +d) + 45

and finally , our max now occurs at t = 0, but we want to move our curve .3 to the right, so the max occurs at t=.3

f(t) = 20 cos (2π/3) (t - .3) + 45

so when does f(t) = 50 ?

20 cos (2π/3)(t - .3) + 45 = 50

cos (2π/3)(t - .3) = .25

so (2π/3)(t-.3) = 1.318116

t - .3 = .62935..

**t = .92935...**

or (2π/3)(t-.3) = 2π - 1.318116

**t= 2.6706....**

of course since the period is 3 seconds, adding or subtracting 3 seconds from any solution will yield a new solution

so how about .92935 + 3 = 3.92935 seconds ??

So the next two times after 2 seconds to reach a height of 50 cm is

t = 2.6706 and t = 3.92935

check:

f(2.6706...) = 50

f(3.92935...) = 50 , used my calculator.

## Answer this Question

## Related Questions

- Pre Calc - I do not see why I got two different equations for my answer A weight...
- precalculus applications - How do I find the equation of a sinusoidal curve from...
- Math - A weight attached to a spring is pulled down so that it is 10 cm from the...
- Math - A weight attached to a spring is pulled down so that it is 10 cm from the...
- asdfds - a car is speeding up and has an instantaneous velocity of 6.0 m/s in ...
- physics - A car is speeding up and has an instantaneous speed of 14.0 m/s when a...
- Physics - A car is speeding up and has an instantaneous speed of 14.2 m/s when a...
- Physics - Two cars pass a school when a stopwatch reads zero. They both travel ...
- physics - Martin caught a fish and wanted to know how much it weighed, but he ...
- Math (PreCalculus) - A spring with a weight attached is oscillating. The weight...

More Related Questions