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The problem asks me to show that the addition of two cosines with different wavelength and frequencies gives a solution with beats. Mathematically, I need to verify that A cos (k1x-w1t)+A cos (k2x-w2t) is equivalent to A cos (.5(k1+k2)x-.5(w1+w2)t) cos (.5(k1-k2)x-.5(w1-w2)t) I converted...

Here's the problem: A damped oscillator has a mass of .05 kg, a spring constant of 5 N/m, and a damping constant of .4 Ns/m. At t=0, the mass is moving at 3.0 m/s at x=.1m. Find x as a function of time. What I have done: I know the damping constant b = .4 and I have used this to find...

Yes...I have the forces for the dx direction to be zero. I'm still doing something wrong though?

I get an answer of 2bL (1- x^2/a^2). This does not seem correct to me, since it contains an x^2 term? Is this right? Is there a substitution I can make for x? x=a or x=L, for instance? This problem is driving me crazy...any help greatly appreciated!

So, for the first segment, dr = dyj. For the second segment, dr = dx i. For the third segment, dr = -dyj. For the fourth segment, dr = -dx i. Is this correct? Are the limits on my integration correct as well? Also, should the answer be 0 (closed path, conservative force...not sure if...

I am asked to calculate the work done by a force as it moves around a path. The force is F = b(1-x^2/a^2)j. The path is a rectangle with coordinates at (0,0); (0,L); (a,L); (a,0). The force moves clockwise around the path beginning at the origin. A diagram is attached. I know work is...

I think that velocity to be v0, not zero. Otherwise, the problem is trivial. I just wanted to check and make sure I wasn't missing anything :smile:

It moves along the x-axis...I forgot to mention that. So gravity is not taken into consideration?

Question answered! Thanks for the input!

Thanks for being so prompt and helpful in your response! So, constrained to move in a circle...that sounds like polar coordinates! So the third term I am missing is the expression of kinetic energy for the disc in polar coordinates? So I should find the center of mass of the disk, and that...

Thanks so much for the help...but I need some further clarification. You said that the contribution to KE comes from the fact that the disk's center of mass can move. How do I express this mathematically as a term in my kinetic energy expression? Is what I have for Kinetic energy thus far...

Lagrange Problem redux -- super urgent... See the attachment to help you visualize this. A rod of length L and mass m is povoted at the origin and swings in the vertical plane. The other end of the rod is attached/pivoted to the center of a thin disk of mass m and radius r. OK, I know that...

We have a rod of length L and mass M pivoted at a point at the origin. This rod can swing in the vertical plane. The other end of the rod is pivoted to the center of a thin disk of mass M and radius R. Derive the equations of motion for the system. I have attached a drawing :) If you...

The system examined in the problem is depicted below: ^^^^^(m1)^^^^^(m2) m1 and m2 are connected by a spring and m1 is connected to the wall by a spring. The spring constant is k. T = m/2 [ x1'^2 +x2'^2 ] kinetic energy of system (x1' is velocity of m1, x2' is velocity of m2) U = 1/2 m...

The problem I am working on asks me to find the curve on the surface z=x^(3/2) which minimizes arc length and connects the points (0,0,0) and (1,1,1). Here's what I did: Integral [sqrt(dx^2+dy^2+dz^2)] Integral [dx sqrt (1+(dy/dx)^2 +(dz/dx)^2] Integral [dx sqrt (1 + (dy/dx)^2 + 9x/4)]...

Lagrangian Dynamics problem -- need help with setup Here's the problem: A simple pendulum of length b and bob with mass m is attached to a massless support moving horizontally with constant acceleration a. Determine the equations of motion. For the pendulum, x = b sin theta and y = b cos...

Two masses connected by a single spring m1 --------m2 I hope this helps to make the geometry clear. I need help with this urgently :)

Please help with this! Harmonic Motion Two masses m1=100 g and m2=100 g slide freely in a horizontal frictionless track and are connected by a spring whose force constant is k=.5 N/m. Find the frequency of oscillatory motion for this system. I know omega = sqrt (k/m), but I have two masses...

Two masses m1=100g and m2=200g slide freely in a horizontal frictionless track and are connected by a spring whoser force constant is k=.5 N/m. Find the frequency of oscillatory motion for this system. Could someone give me a hint/help me get started on this? What equation(s) should I...

Evaluating indefinite integral -- toughie! I have the velocity function v(x) = [(k*x^2)/(2*m)] + v0 I need to integrate this to get position as a function of time. So v = dx/dt. Separating variables, I get t = Integral [2m/(2mv0 + kx^2)] Here's where I'm stuck...If i pull out the 2m, then I...

Thanks for the input!

Need urgent help -- projectile motion with air resistance Consider a projectile fired vertically in a constant gravitational field. For the same inital velocities, compare the times required for the projectile to reach its maximum height (a) for zero resisting force and (b) for a resisting...

Projectile Motion with air resistance -- need urgent help Consider a projectile fired vertically in a constant gravitational field. For the same inital velocities, compare the times required for the projectile to reach its maximum height (a) for zero resisting force and (b) for a resisting...

Projectile Motion -- need urgent help :) If a projectile is fired from the origin of the coordinate system with an initial velocity v and in a direction making an angle alpha with the horizontal, calculate the time required for the projectile to cross a line passing thorugh the origin and...

Calculate the average value of the curl of the fluid for a rectangular path 15 cm by 10 cm, as shown in the figure (see file attachment). Va=(10i + 5j) Vb = (5i+10j) Vc= (5i + 10j) Vd = (10i + 5j) Could someone help me to get started with this one? Please :smile: Maybe give me an...

I know that rate of flow is equal to pi*(P1-P2)*R^4/8nL. For blood in the coronary artery, I know the pressure drop, and the radius of the artery. What is the viscosity of blood? I can't find this value anywhere! And what value should I enter for L (distance L along a tube)? Is there an...

Here goes: A potential customer for an 85000 dollar fire insurance policy possesses a home in an area that according to experience, may sustain a total loss in a given year with probability of .001 and a 50% loss with probability .01. Ignoring all other partial losses, what premium shoud the...

I understand 2a now! But could you elaborate a little more on the first problem? How do I start?

If someone could gtive me a general idea about how to approach these problems, I would be very grateful! Our class time was devoted to derivation rather than application. 1) Find the angle between the surfaces defined by r^2=9 and x+y+z^2=1 at the point (2,-2,1). 2) The height of a hill...

What is the dot product of a unit vector (e) with a non-unit vector (A)? Is this some sort of identity? Thanks, don_anon25

Question answered! Thanks!

These problems are actually for my classical mechanics class, but they are linear-algebra based. I can construct a transformation matrix, but I have trouble visualizing the rotations, particularly in 3-space. So if someone could help me get a pictorial idea of what's actually happening, then...

Here's my problem: An ideal gas is allowed to expand freely into an evacuated chamber. The gas is at a pressure of 5 bar and a temperature of 45 degrees Celsius. Find the final temperature and pressure of the gas. Find the entropy produced. W=0, Q=0, dU=0, and dT=0. So the final temp. is...

Is there a different approach to this problem other than the one I've taken? I know: Q=0, W=0, dU=0, p1, and T1=T2. How do I get p2?

The problem is that I only have the temperature and pressure of the entering gas, and no other data. Any ideas? Here's the actual problem: An ideal gas is allowed to expand freely into an evacuated chamber. The pressure of the entering gas is 5 bar and it has a temperature of 45 degrees...

For the free expansion of an ideal gas into an evacuated chamber, I know that Work=0 and Q=0. Correct? This implies that the change in internal energy dU also equals 0. Since U depends solely on T, this should mean that the final temperature of the chamber is equal to the temperature of the...