Understanding Simple Harmonic Motion with Position and Acceleration Graphs

[physks4dumies]

Homework Statement

Using the acceleration as a function of time graph, we are required to sketch the position as function of time graph

Homework Equations

I know that the position vs. time graph is a cosine wave and the aforementioned is a sine wave. I have NO idea how to start considering there are no numbers involved.

The Attempt at a Solution

I tried to plot the point of the a vs time graph corresponding to the position...only 1/4 back. In the end, i got a graph that looked EXACTLY like the first. help?

 

[rock.freak667]

if $a=-\omega^2 x$

it is possible to write x as a function of time...$x=x_0 sin(\omega t)$

 

[lasershadow]

I think this is meant to be in variables.
http://euclid.hamline.edu/~arundquist/latex/showequation.php?eqn_id=31336
so given the definition of the cosine graph, we know the amplitude and the period.

 

[physks4dumies]

well since the a vs t graph is a cosine function, wouldn't the x vs. t graph be a negative cosine function? (basically the same thing--inverted?)

 

[DylanB]

well since the a vs t graph is a cosine function, wouldn't the x vs. t graph be a negative cosine function? (basically the same thing--inverted?)

correct, though not entirely. the position graph will be adjusted by some constant. take a look at rockfreaks equation, what is it?

 

[physks4dumies]

ooh i understand it now! Thanks eeryone