On an airtrack, a cart oscillates between the 10 cm mark and the 85 cm mark completing 13 oscillations in 3 minutes. Find the frequency, period, amplitude, maximum speed and minimum acceleration of the cart.
First question, should my calculator be in radiant or degree mode?
I know how to find the period, frequency and amplitude. How do I find the maximum speed and minimum acceleration?
f= 13rad/180s = 0.072rad/s
T=1/(13rad/180s)= 13.8462 Hz
Amplitude= (85cm-10cm)/2 =0.375m
I'm not sure what the next step should be to find the maximum speed and the minimum acceleration. Here is what I have...
ω= 2πf = ω=2π(0.072) = 0.453 rad/s
To find the speed do you use v(t)=-ωAsin(ωt)
If so then v(t)=(-0.453 rad/s)(0.375m)sin(0.453rad/s*13.8462s)
the answer would be: -0.041m/s
Or should I use:
v(max)=+/- ωA this would simply be (0.453rad/s)(0.375m)= 0.17 m/s
Then for the acceleration I think the equation is: a=-ω^2Acos(ωt)
If this is the right equation then to plug in the numbers it would look like:
a=(-0.453rad/s)^2*(0.375m)cos(0.453rad… -0.077 m/s^2 (again, does this look right and how do I know if that is the minimum acceleration?)
or can I use A(max)= +/- ω^2A this would be -(0.453rad/s)^2*(13.8462s) = -2.84m/s^2 (for min use the negative answer?)
Anyone willing to look this over and help out would be very appreciated! Which equation is right for finding maximum speed and minimum acceleration? And if I totally messed this up can you try to explain it a bit?
Thank you!!!
*sorry if I missed any units, I tried to get them all in there.
First question, should my calculator be in radiant or degree mode?
I know how to find the period, frequency and amplitude. How do I find the maximum speed and minimum acceleration?
f= 13rad/180s = 0.072rad/s
T=1/(13rad/180s)= 13.8462 Hz
Amplitude= (85cm-10cm)/2 =0.375m
I'm not sure what the next step should be to find the maximum speed and the minimum acceleration. Here is what I have...
ω= 2πf = ω=2π(0.072) = 0.453 rad/s
To find the speed do you use v(t)=-ωAsin(ωt)
If so then v(t)=(-0.453 rad/s)(0.375m)sin(0.453rad/s*13.8462s)
the answer would be: -0.041m/s
Or should I use:
v(max)=+/- ωA this would simply be (0.453rad/s)(0.375m)= 0.17 m/s
Then for the acceleration I think the equation is: a=-ω^2Acos(ωt)
If this is the right equation then to plug in the numbers it would look like:
a=(-0.453rad/s)^2*(0.375m)cos(0.453rad… -0.077 m/s^2 (again, does this look right and how do I know if that is the minimum acceleration?)
or can I use A(max)= +/- ω^2A this would be -(0.453rad/s)^2*(13.8462s) = -2.84m/s^2 (for min use the negative answer?)
Anyone willing to look this over and help out would be very appreciated! Which equation is right for finding maximum speed and minimum acceleration? And if I totally messed this up can you try to explain it a bit?
Thank you!!!
*sorry if I missed any units, I tried to get them all in there.
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