It is just as belliott4488 described. There is not much more significance to B and C than that.
If you rewrite the equation given in the form y = At^2 + Bt + C, into the form
y = A'(t-tb)^2 + B'(t-tb) + C', where tb is the time of the bounce being considered... then A' is the...
No. don't substitute in an x.
2pi/.80 = 7.854
You need the function:
y = acos(7.854x) + acos(7.854x - 0.7854)
don't substitute in an x... you need to find the amplitude of this function... you can write this sum of two cosines as a single cosine...
try to use this identity. cosA...
I'm sorry. A is not 80... amplitude is unknown variable a. I should have written wavelength is 80cm.
I'm getting a phase difference of -0.7854 radians
Using these and adding
y = a cos (kx) to
y = a cos (kx + phi)
where phi = -0.7854 and k = 2pi/0.80 = 7.854
you can get the...
You can choose any point for the torque pivot... It's best to choose a point that makes your equations simple...
I recommend the upper right point, because then you avoid having the trig stuff in your equation.
Your answer to the first question looks good to me.
But your answer to the second question doesn't. In the first question... you were together with the mirror... whether you were still or moving... you and the mirror were in the same inertial frame of reference. Like you said, the laws of...
Yes, you're right. N must equal L to get the equation you have:
y(N) = 2y sin((Npix)/L)cos((vNtpi)/L)
y = 0.023sin(xpi)cos(0.714 pi t)
So N = 7.
Another way to look at it... Find the angle at the end of the standing wave... The angle is xpi... that's coming from...
V(R) - V(infinity) = -\int_{\infty}^{R}\vec{E}(r)\cdot\vec{dr}
This is just the definition of electric potential.
V(infinity) = 0, so:
V(R) = -\int_{\infty}^{R}\vec{E}(r)\cdot\vec{dr}
Use your formula for E(r) from part a). Solve the integral.
Draw a sketch... first draw the reflections of the point source in the two mirrors... what are the coordinates of these two images. I'll call the I1 (reflection in mirror 1) and I2 (reflection in mirror 2). Now I1 and I2 also have reflections... I1 has a reflection in mirror 2... call it I12...
Yes, use energy... the work done by friction is the same each time the object crosses the rough surface. Use the initial energy... and the work by friction per trip across the rough surface... to get the number of trips before energy of the box becomes zero.
Generally uniform circular motion means a constant speed throughout the circle...
In the case of a ball attaches to a string going through a vertical circle... you don't have uniform circular motion... however at the top and bottom we do have dv/dt = 0 where v is the speed of the ball...
You have the formula for the time constant T = L/R. You need the time constant to become half... so what do you need the R to become?
The steady state value of the current is Vo/R. considering the change in R above, what do you need to do to Vo to keep the same steady state current as before...
Yes, that's the right equation.
I still don't understand... why do you need the second derivative with respect to x, or with respect to time? you need the amplitude at a certain x value right?
you've got the equation of the standing wave.
y(x,t)=(Asinkx)sinwt
The amplitude at any x...
You can use energy conservation... During oscillation, the top and bottoms are when v = 0... ie at those points, kinetic energy is 0.
For simple harmonic motion we need the mass to return to the same maximum height (that's what makes it simple harmonic motion)...
at that maximum height...
Yes, k = 980 N/m as you calculated.
And the minimum x' seems to me to be -0.05 - 0.15 = -0.20m
The equilibrium position is -0.05m. So the max is -0.05+0.15m = 0.10m.
And the minimum position is -0.05-0.15 = -0.20m. Is this the wrong answer?