Oscillator Questions: Center Position, Amplitude & Period Calculations

[wolves5]

The position of the center of the box shown is given by the equation:
x = 4.4 m * cos(29/sec * t)

(a) What is the position of the box 2 seconds after the oscillations have started?
x = m
I don't know how to start A. I plugged in 2 seconds for t in the above equation, but my answer is not right.

(b) What is the amplitude of the box's oscillations?
The amplitude is 4.4 and it's correct.

(c) What is the period of the box's oscillations?
The period is 0.21666 seconds and its correct.

(d) What is the box's maximum velocity?
The max velocity is 127.6 m/s and its correct.

(e) What is the box's maximum acceleration?
The max acceleration si 3700.4 m/s2 and its correct.

(f) How long does it take the box to move from -2.2 m to +2.2 m?
I don't know how to approach this one either.

 

[lewando]

x = 4.4 m * cos(29/sec * t)

What is "sec"?

 

[wolves5]

seconds?

 

[lewando]

What did you get for part a?

 

[wolves5]

I did 4.4 * cos(29*2)= 2.33164. But this is not the right answer.

 

[lewando]

standby, please...cockpit trouble

 

[wolves5]

How do you do that when there's no units for the numerator? I tried doing 4.4 * cos (2pi/29 * 2), but that didnt work. How do you convert it?

 

[lewando]

"29/sec" is most likely Hertz (cycles/sec). Need to convert this to rad/sec. 1 "cycle" = 2pi rad. So multiply 29 cycles/sec * 2pi rad/cycle.

 

[wolves5]

Alright, when I converted it, my final answer was 4.386885896 and that is not right.

 

[lewando]

I got 4.4 (3.999 considering SDs)

 

[wolves5]

Its still not right. I don't understand any other way to solve for it.

 

[lewando]

Is there anything special about "the box shown"? I am imagining a box attached to a device that makes it oscillate according to the described function. Does it start at x=0? EDIT: when t=0 where is the box?

 

[wolves5]

I attached the picture. Can you see it? Its supposed to be an attachement.

 

[gneill]

You might consider that 29*t/sec yields radians. No conversion required. What's 4.4m x cos(29 x 2 radians) ?

 

[wolves5]

I got 2.331644763, which is also not correct.

 

[gneill]

I got 2.331644763, which is also not correct.

That would be the result for 2*29 DEGREES. Try 2*29 RADIANS. Is your calculator set to degrees mode?

 

[lewando]

So per equation, someone pulls the box out to the right to a 4.4m hash mark then let's go at t=0.

If 29 is in Hz, the result should be 4.4m
If 29 is in rad/sec, the result should be 0.52m (I don't think you checked this)

Is your answer checker caring about SDs tightly? Maybe "2 seconds" implies 1 SD.

Running out of secret weapons.