- #1
NutriGrainKiller
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This is a problem right out of the book. My professor worked it out in class but now that I look over it I'm not sure why he chose the method he did. This is the problem exactly as it is stated in the book:
f=2.5Hz
T=.4sec
w=15.71rad/sec
Problem #1
Now, I get confused in several places. First, my professor states that as a given Xi=+1.1cm and Vi=-15cm/s. Can someone explain to me [in words] how he took the position at t=0 and assumed them values of Xi and Vi?
Problem #2
We were given these three formulas:
{keep in mind 'o' is phase offset or "phi"}
x(t) = A*Cos(wt+o)
v(t)=A*w*Sin(wt+o)
a(t)=A*w^2*Cos(wt+o)
Now from this my professor said this: a = -w^2*X => ai = -w^2*Xi -this ends up being -2.71 m/s^2
Problem #3
He continued to find "phi" or the phase offset. Here is what he did: arctan(Vi/WXi). This equation is right out of the book, and so far I have only seen it in this exact form. I understand how it was derived, but will it ever be needed in a different form?
Thanks guys!
From this I was able to derive several other components that will be very helpful for solving this problem. Here are the givens:The point of the needeld of a sewing machine moves in simple harmonic motion along the x-axis with a frequency of 2.5Hz. At t=0 its position and velocity components are +1.1cm and -15cm/s.
a) Find the acceleration component of the needle at t=0
b) Write equations giving the position, velocity, and acceleration components of the point as a function of time
f=2.5Hz
T=.4sec
w=15.71rad/sec
Problem #1
Now, I get confused in several places. First, my professor states that as a given Xi=+1.1cm and Vi=-15cm/s. Can someone explain to me [in words] how he took the position at t=0 and assumed them values of Xi and Vi?
Problem #2
We were given these three formulas:
{keep in mind 'o' is phase offset or "phi"}
x(t) = A*Cos(wt+o)
v(t)=A*w*Sin(wt+o)
a(t)=A*w^2*Cos(wt+o)
Now from this my professor said this: a = -w^2*X => ai = -w^2*Xi -this ends up being -2.71 m/s^2
Problem #3
He continued to find "phi" or the phase offset. Here is what he did: arctan(Vi/WXi). This equation is right out of the book, and so far I have only seen it in this exact form. I understand how it was derived, but will it ever be needed in a different form?
Thanks guys!