Please provide the derevation of the analytical formula used to calculate the damping coefficient
132338
Any  mass-spring system with viscous damping added gives the characteristic quadratic response if the damping force/torque is proportional to velocity. Method to adopt is to draw the block diagram showing the mass-spring system with velocity dependent restraining force as a feedback term.  Block diag gives good visual picture, or you can write eqns of motion down write away if you want.\nAnswer will look something like:         \n  1/(s/wn^2+(2z/wn)*s+1), where wn=undamped natural frequency,\nz is the damping coefficient, and s=j*w in steady- state.\nDamping term will lower the frequency somewhat,and of course z=0.7 is critical damping,no overshoot.
422742
.  Electrical resonance is not generally related to mechanical resonance.  It would be possible, with considerable calculation and inventiveness to put together a device which vibrated in time with or at a harmonic fraction of its electrical resonant frequency, but it would be a real academic undertaking.\n.  There is no single equation to calculate the resonant frequency of "an object".  If you narrowly define the object as say "a taut string" or "a circular plate", equations of only a few terms can be derived for each of those cases, but the equations would not be the same for different cases.  There would be similarities, but they would have diffent constants and different variables.  Most objects would require the development of a complicated mathematical description of the interelatedness of the masses, elastic properties, dimensions, stiffnesses and coupling mechanics of the various components of the object in order to calculate a resonant frequency.  For some complex objects, which are dominated by a single large and simple structure, like say the cylindrical fuselage of an airplane, there are formulae to calculate the resonant frequency.  For objects like suspension bridges, or cable stayed bridges or skyscrapers, it is necessary to go through the pains of developing a mathematical model to find a range within which the object will resonate.  For most objects, you just build it, test it and then do something to eliminate undesirable resonances.\n.  Pretty much the same can be said about calculating the electrical resonance of an object.\n.  For simple resonant circuits there are straightforward formulae for calculating their resonant frequencies, but the formulae are different for different types of resonant circuits.  Whatever text I might have on resonance of electrical circuits is buried in a box somewhere, but should be able to find a book which includes these formuale and other electrical formulae at a college library, online or maybe even at some place like Radio Shack®.
368294
a = (v_f - v_i)/t\n-0.25g = (0-v)/t\n0.25g = v/t\nt = 4v/g\n\nd = v*t + 0.5*a*t^2\nd = v*4v/g + 0.5*(-0.25g)*(4v/g)^2\nd = (4v^2)/g - 0.125 *g* (16 v^2 )/g^2\nd = (4v^2)/g - (2v^2)/g\n\nd = (2*v^2)/g
482439
a)  w = sqrt(k/m) where w is in rad/s. Therefore force constant k = 473 N/m\nb) period = T = 1/f = 0.5 sec\n\nX = Asin(wt) = A*sin(sqrt(k/m)*t) If you differentiate that, you get speed, differentiate again and you get acceleration.\n\nc) v = A*sqrt(k/m)*cos(sqrt(k/m)*t) The max speed would be at the time that the cos evaluates to equal 1.\nd) a = -A*(k/m)*sin(sqrt(k/m)*t) Max when sin = 1\n\nNote: if you leave A in cm, your speed and acceleration will be in cm.\n\nCheck out http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html#c1 and all the links it gives you.
157307
The only link you need:\n\nhttp://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html\n\nHint:  look under "Mechanics"
483545
I have already answered part 1. in another question you've asked. I think you probably didn't use the right units (like cm needs to be convered to meters) and got the wrong answer.\n\nNow for part 2:\n\nInduced EMF, ℰ = -L(di/dt)\n\nwhere i is the current and L is the inductance\n\nWe are given that the magnitude of the induced current,\n\ndi = 47 mA\n\nand the oscillation frequency is 100 Hz. This means that dt = 1/f = 0.01 sec\n\nWe have L = 8.44 × 10-^3 henries from before\n\nSo |ℰ| = L(di/dt) = -(8.44 × 10-^3)(0.047)/(0.01) = 0.0397 volts\n\n------------------------------------------------------\n\nNow part 3 has to do with mutual inductance:\n\nVs = VpNs / Np\n\nwhere \n\nVs is the voltage across the secondary inductor, \nVp is the voltage across the primary inductor (the one connected to a power source), \nNs is the number of turns in the secondary inductor, and \nNp is the number of turns in the primary inductor. \n\nTherefore Vp = VsNp/Ns and Vs = 0.0397 volts as calculated before, so\n\nVp = (0.0397)(197)/(2920) = 0.00268 volts
531172
you started right with the quotient rule (BT-TB/B^2), but the deriv of Tanx - 1 = sec^2 x, the -1 goes away as the dervi of a constant is zero (on the other hand, the dervi of a coefficient is that coefficient).  That is the critical mistake I saw... and changing that will change your whole answer. Just scratch it out and try again!
491976
put x=2 directly into the given equation to get value of x at t=2...the answer u get is the displacement\n\ndifferentiate the equation wrt time to get velocity equation and then differentiate the velocity equation to get acceleration equation\n\nin both cases put t=2 to get velocity and acceleration\n\nconvert the given equation in terms of sin\ncomparing the new equation with x=asin(wt+@)\nwhere a=amplitude\n          w=angular frequency\n          @=phase\n\nalso use equations w=2 x pi x f and T=1/f\nhere x denotes multiplication \nf=frequency \nT=period
279396
For a column of vibrating air with one closed end and one open end the equation is:\n\nlambda = 4L\n\nWhere L is the length of the tube and lambda is the wavelength of the standing sound wave.  Given the fact you know the frequency, and the speeed of sound, I think you can figure out the rest.
615273
F = d/dt(mv) [the time deravitive of the momentum] = dp/dt  where p is the momentum\n\nWork = Energy = F x distance\n\nPower = Energy/time\n\nPower = (F x distance)/time\n\nPower = [(dp/dt) x distance]/t\n\nremember dp/dt = d/dt(mv) = m dv/dt + v dm/dt
439565
There are a few things to keep in mind here: all of the energy in the initial system is rotational, and the initial energy is equal to the energy lost to friction. Also note that the energy is lost to friction at a constant rate.\n\n(a) The initial energy of the system is:\n\nE = (1/2) * I * w²\n\nWhere I is the moment of inertia and w is the angular velocity. The power transferred from the system due to friction is equal to the time derivative of the energy loss:\n\nP = dE/dt = I * w * a\n\nwhere a is the angular decceleration.\n\nSince the power is transferred at a constant rate and removes all of the energy from the system, we can take this as:\n\nP = -E/t (negative sign denotes power loss)\n\nCombining the power equations yields:\n\nI * w * a = -E/t\n\nSolving for a:\n\na = -E / (I * w * t)\n\nFinally, substitute the expression for E to obtain:\n\na = -I * w² / (I * w * t)\n\na = -w/(t)\n\nSubstituting the values yields:\n\na = -(300 rev/min * 2*pi rad/rev * 1/60 min/sec)/(2.5 hr * 3600 sec/hr)\n\na = -(31.42 rad/s)/(9000 s)\n\na = -.00349 rad/s²\n\n(b) The rotational behavior of the fly wheel can be modeled as simply:\n\nR(t) = -1/2*a*t² + w*t + Ri\n\nwhere R(t) is measured in radians and Ri is the initial angular displacement. Assuming that Ri = 0 (we'll measure the number of rotations from its initial position), then the flywheel will revolve:\n\nR(t) = -1/2*a*t² + w*t  (radians)\n\nR(t) = (-1/2*a*t² + w*t)/(2 * pi)  (revolutions)\n\nSubtituting the values:\n\nR(2.5 hr) = R(9000 s) = (-.5*.001745*(9000 s)² + (31.42 rad/s)(9000 s))/(2*pi)\n\nR = 22500 revolutions\n\n(c) The tangential component of the linear acceleration of a point on a rotating body is given as:\n\nA-tangent = a * r\n\nwhere A = linear acceleration. The angular acceleration is constant, so for all w (including w=75 rev/min), the linear acceleration will also be constant. Thus:\n\nA-tangent = (-.00349 rad/s²)(.5 m)\n\nA-tangent = -1.745 x 10^(-3) m/s²\n\nA-tangent = -1.745 mm/s²\n\n(d) The magnitude of the net linear acceleration on the particle is composed of a tangential and a normal component. The equation is of the form:\n\nAnet = [ (A-tangent)² + (A-normal)² ]^(1/2)\n\nOr:\n\nAnet = [ (a*r)² + (v-tangent²/r)² ]^(1/2)\n\nNote that the tangential velocity is given by:\n\nv-tangent = w * r\n\nThus, the magnitude of net linear acceleration is:\n\nAnet = [ (a * r)² + (w² * r)² ]^(1/2)\n\nSubstituting the known values yields (note that for this case, the angular velocity of 75 rev/min is equal to 7.854 rad/s):\n\nAnet = [ (-.00349 * .5)² + (7.85² * .5)² ]^(1/2)\n\nAnet = 30.84 m/s²\n\nFINAL ANSWERS:\n\n(a) a = -.00349 rad/s²\n(b) R = 22500 revolutions\n(c) A-tangent = -1.745 mm/s²\n(d) Anet = 30.81 m/s²
469984
Coefficients are:  1  1  3
410160
Wow. Your classmate just asked this question. But here's your answer anyways...\n\nThere are a few things to keep in mind here: all of the energy in the initial system is rotational, and the initial energy is equal to the energy lost to friction. Also note that the energy is lost to friction at a constant rate.\n\n(a) The initial energy of the system is:\n\nE = (1/2) * I * w²\n\nWhere I is the moment of inertia and w is the angular velocity. The power transferred from the system due to friction is equal to the time derivative of the energy loss:\n\nP = dE/dt = I * w * a\n\nwhere a is the angular decceleration.\n\nSince the power is transferred at a constant rate and removes all of the energy from the system, we can take this as:\n\nP = -E/t (negative sign denotes power loss)\n\nCombining the power equations yields:\n\nI * w * a = -E/t\n\nSolving for a:\n\na = -E / (I * w * t)\n\nFinally, substitute the expression for E to obtain:\n\na = -I * w² / (I * w * t)\n\na = -w/(t)\n\nSubstituting the values yields:\n\na = -(150 rev/min * 2*pi rad/rev * 1/60 min/sec)/(2.2 hr * 3600 sec/hr)\n\na = -(15.71 rad/s)/(7920 s)\n\na = -.001983 rad/s²\n\n(b) The rotational behavior of the fly wheel can be modeled as simply:\n\nR(t) = -1/2*a*t² + w*t + Ri\n\nwhere R(t) is measured in radians and Ri is the initial angular displacement. Assuming that Ri = 0 (we'll measure the number of rotations from its initial position), then the flywheel will revolve:\n\nR(t) = -1/2*a*t² + w*t (radians)\n\nR(t) = (-1/2*a*t² + w*t)/(2 * pi) (revolutions)\n\nSubtituting the values:\n\nR(2.2 hr) = R(7920 s) = (-.5*.001983*(7920 s)² + (15.71 rad/s)(7920 s))/(2*pi)\n\nR = 9900 revolutions\n\n(c) The tangential component of the linear acceleration of a point on a rotating body is given as:\n\nA-tangent = a * r\n\nwhere A = linear acceleration. The angular acceleration is constant, so for all w (including w=75 rev/min), the linear acceleration will also be constant. Thus:\n\nA-tangent = (-.001983 rad/s²)(.5 m)\n\nA-tangent = -9.915 x 10^(-4) m/s²\n\nA-tangent = -0.9915 mm/s²\n\n(d) The magnitude of the net linear acceleration on the particle is composed of a tangential and a normal component. The equation is of the form:\n\nAnet = [ (A-tangent)² + (A-normal)² ]^(1/2)\n\nOr:\n\nAnet = [ (a*r)² + (v-tangent²/r)² ]^(1/2)\n\nNote that the tangential velocity is given by:\n\nv-tangent = w * r\n\nThus, the magnitude of net linear acceleration is:\n\nAnet = [ (a * r)² + (w² * r)² ]^(1/2)\n\nSubstituting the known values yields (note that for this case, the angular velocity of 75 rev/min is equal to 7.854 rad/s):\n\nAnet = [ (-.001983 * .5)² + (7.85² * .5)² ]^(1/2)\n\nAnet = 30.81 m/s²\n\nFINAL ANSWERS:\n\n(a) a = -.001983 rad/s²\n(b) R = 9900 revolutions\n(c) A-tangent = -0.9915 mm/s²\n(d) Anet = 30.81 m/s²
493617
well since a is constant well say\na(t) = a\nintegrate\nint[a(t)]=v(t)= a*t + C  where C=initial velocity v0\nintegrate again\n=s(t) = (a/2)t^2 + v0t + D where D=initial displacement s0\n\nand thats how its derived in general terms
157524
detlaH=H(products) - H(Reactants)\n\n200KJ/mol
85259
Use free body diagram to balance the forces and u can derive the equation of motion \nIf u want i can give u full derivation.\n"::
453548
I understand your frustration in receiving no Answer yet to this question, but since I do not have any direct knowledge of how to perform the calculation(s) you need ... I hope the link below serves you well.  It appears to explain the mathematics behind all the concepts you mention.