# trig

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?

1. 👍 0
2. 👎 0
3. 👁 230
1. 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.

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### Math

A weight attached to a spring is pulled down so that it is 10 cm from the floor and is released so that it bounces up and down. When the effects of friction and gravity are ignored. It's height can be modeled by a sine function of

asked by Safaa on March 6, 2012
2. ### Math

A weight attached to a spring is pulled down so that it is 10 cm from the floor and is released so that it bounces up and down. When the effects of friction and gravity are ignored. It's height can be modeled by a sine function of

asked by Safaa on March 6, 2012
3. ### Physics

A vertical spring has one end attached to the ceiling and a 2.50 kg weight attached to the other one. When the system is at rest, the spring is stretched by 20.0 cm. Now let the weight drop from a position in which the spring is

asked by Timo on June 29, 2011
4. ### College Algebra

Hooke's Law states that the distance a spring stretches is directly proportional to the weight attached to the spring. If a 30-pound weight attached to the spring stretches the spring 8 inches, find how much weight is needed to

asked by BFG on July 10, 2012
5. ### Physics

Three different masses are attached to a spring which hangs down vertically from the ceiling. A metric ruler hangs from the ceiling next to the spring and measures how far from the ceiling the sping hangs. When a 110 N weight is

asked by Morgan on October 25, 2016
1. ### Math

A plumber charges \$45 for a service call, plus \$70/h for her time. a. Find the cost of a two hour service call. b. How long was a services call that cost \$150? Also ....... as the weight held by a spring increases, the length of

asked by Jessica on April 19, 2011
2. ### precalculus applications

How do I find the equation of a sinusoidal curve from just knowing the lowest point and highest point of it? For example: A weight attached to the end of a long spring is bouncing up and down. If we do not worry about friction,

asked by Jimmy on March 21, 2008
3. ### Math

The distance a spring stretches is directly proportional to the force applied to the spring. A 4-lb weight stretches a spring 20 in. A 16-lb weight stretches a spring 26 in. Find the length of the spring with no weight attached.

asked by Chase on May 4, 2011
4. ### Math

as the weight held by a spring increases, the length of the spring increase proportionally. suppose a 2-lb weight stretches a spring to 15 in., and a 12-lb weight stretches the same spring to 20 in. what is the length of the

asked by Ronnie on April 4, 2012
5. ### Physics

you strike a huge spring at a speed of 30m/s while strapped in a steel cage. When you hit the spring with combined mass of 320kg it is compressed 9.0m. A) What is the spring constant of the spring? B) How long are you in contact

asked by Sierra on February 22, 2016

More Similar Questions