Hard calculus question
The height of an oscillating object follows Damped Harmonic Motion. The formula for height is
h(t) = -0.3e^-0.4t * cos(4*pi*t) where t = seconds and h(t) = meters and pi = 3.14159.......
a) The height is a distance measure. What formula would give us the instantaneous VELOCITY?
b) What is the first POSITIVE time t that gives us a maximum velocity?
April 17, 2015
13 Comments • Newest first
Height is a position. Derivative of position (in this case height) is velocity.
So... given h(t) is your original equation.
A) Find h'(t). Derive your first equation to get the velocity.
B) Find where h'(t) = 0. Find the roots of the equation. If before-and-after a root, it changes from positive-to-negative, you have a maximum. If it changes from negative-to-positive at a root, you have a minimum.
aw. i was hoping there was an actual hard math problem to solve.
0.12e^-0.4t*cos(4pit)+1.2e^-0.4t*sin(4pit) is the the velocity equation (derivative of your height function).
If you don't know what we are talking about and haven't learned this, it might be just asking you to find the instantaneous rate of change (IROC) but it is far enough into the year so you should have learned derivatives.
Lel in my diff eq class we have to derive those harmonic motion equations.
@Shini: Calculus really isn't that hard. You'll most likely learn some calculus before you leave high school.
I'm sooo not looking forward to college. That's some intimidating math.
PRODUCT RULE
but seriously, y=a'b+ab'
I'm too dumb for such things.
On a calc take the derivative thats a then graph to see when line is about the x axis.... its easy unless its a trick question
If you need help on your homework just say you need help on your homework.
It is obviously a line integral.
derivative of the first times the second + derivative of the second times the first
You can't be serious OP.
Did you not learn product rule or something.
I don't know, it's too hard. I don't know how to take the derivative of that monster.