How Do You Find Displacement, Velocity, and Acceleration in Oscillatory Motion?

[nemzy]

Question:
A 1.00 kg object attached to a spring of force constant 41.0 N/m oscillates on a horizontal, frictionless track. At t = 0, the object is released from rest at x = -3.00 cm. (That is, the spring is compressed by 3.00 cm.)

Find the displacement, velocity and acceleration as functions of the time t.



my answer:

my legend:
w= angular frequency
&= phase constant

ok, so for displacement: x(t)=Acos(wt+&)
velocity: -wAsin(wt+&)
acceleration: -w^2Acos(wt+&)

A = max displacement, which is .03 m in this case

w= 2(pi)(f)

where f=1/T

where T=2(pi)(square root of m/k)

so solving for all that, i get w=6.41 which i know is right...

so now how do i solve the question?? HOw do i solve each of those equations as a function of something? i have no idea how to do this, i been stuck on this problem forever and i keep getting the wrong answer

thanks

 

[dextercioby]

1.If the mass and the elestic constant is give,then it's given $\omega$

2. Take the general solution for the periodic motion
$$x(t)=A\sin(\omega t+\phi)$$
and impose the codition that,at the initial time,the x must be "-A".You'll get the phase.Then to get 'v' and 'a' u need to differentiate wrt time.


Daniel.

 

[nemzy]

do you mean cos instead of sin??

also a quick quesiton, when calculating, do i use radian or degree mode in my graphing calc?

thx

 

[dextercioby]

1.The anwer will come out with "-cos".
2.I don't know what will work with your computer...

Daniel.

 

[PICsmith]

Use radians for your calculator unless you're very sure that you're working with degrees.