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[Hero]

More specifically, oscillations, springs, waves, etc.

Just having difficulty with a few of these.

Any help would be appreciated.

1. A 2.00 kg mass vibrates according to the equation x = .650 cos 8.40t where x is in meters and t in seconds. Determine a) the amplitude, b), the frequency, c) the total energy and d) the kinetic energy and potential energy when x = .260 m.

2. A glider on an air track is connected by springs to either end of the track.

|----[ M ]--------|
k k

Both springs have the same spring constant, k, and the glider has mass M.
a) Determine the frequency of the oscillation, assuming no damping, if k = 100 N/m and M = 200 grams. b) It is observed that after 55 oscillations, the amplitude of the oscillation has dropped to one half of its initial value. Estimate the value of a. c) How long does it take the amplitude to decrease to one quarter of its initial value?

3. A block of jello rests on a cafeteria plate. You pust it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus of jello is 520 N/m^2 and its density is 1300 kg/m^3.

There's a picture and the jello cube is 4 cm tall, 8 cm long, and 8 cm wide.

 

[Phoenix]

I don't normally do homework threads, but I'll help you out as much as I can. What specific help do you need?

 

[Dilbert]

In the future -- ESPECIALLY with physics problems -- it would be very helpful to explain exactly where you are stuck. If there is a specific concept you're having trouble with, it's easier to give a "nudge" rather than a solution.

1. A 2.00 kg mass vibrates according to the equation x = .650 cos 8.40t where x is in meters and t in seconds. Determine a) the amplitude, b), the frequency, c) the total energy and d) the kinetic energy and potential energy when x = .260 m.

The generic form of the wave equation is

x = A sin (or cos) wt

where x = displacement, A = amplitude, w = angular frequency, and t = time.

a) By comparison with the general wave equation, the amplitude is .650 meters.

b) Angular frequency is related to frequency: f = w/(2*pi) (This makes sense with dimensional analysis: angular frequency is given in radians per second, frequency is in Hertz, which is 1/seconds, and 2*pi is the number of radians in a complete circle.)

So, f = 8.40/(2*pi) Hz. You can break out the calculator...I'm too lazy.

c) Total energy = potential energy + kinetic energy. With a spring, PE is measured with respect to displacement from an inital position. When the spring is at the maximum displacement, PE is at a max and KE is zero, so PE = TE. When the spring is at the zero displacement location, then KE is at a max and PE is zero, so KE = TE. Use either of those two points to calculate the total energy.

For a (massless) spring, normally you can calculate PE directly by using the point of maximum displacement: PE = ½kx² where x = x_max. However, unless you remember the formula for calculating the spring constant, you might want to use another method. (I think it's related to frequency, but you'll have to look it up.) You can take the derivative of displacement to find the equation for velocity: dx/dt = v(t) = -Aw sin wt. The maximum value of v(t) would correspond to the the point at which KE = the total energy of the system, so you can use KE = TE = ½mv².

d) At some arbitrary point, you can use the v(t) equation to find the KE, and since you just found the TE in part c) of this problem, you can use the relationship PE + KE = TE to find the PE.

As for problem 3, that would be the most interesting one to solve. Remember that oscillatory motion results from any restoring force of the form F = -kx. In this case, the force is being provided by the shear modulus of the Jello. If you can figure out this force, then you can equate it to a "spring constant," and start writing the more familiar equations.

Hope this helps...I gotta go get some coffee now.

 

[ManDudeChild]

Funny this topic should pop up. Lately I've found myself really interested in magnetism and so forth. Do either of you know of some good books that are n00bish (as I'm not well versed on the subject) so I can start learning?

 

[fart]

does it bother anyone else that this isn't e&m?

 

[Dilbert]

does it bother anyone else that this isn't e&m?

I was wondering myself for a couple of seconds, but it DOES make sense. Most lower-level EM classes I took started out by refreshing the physical analogues to EM phenomena to help build intuition before pushing on to newer things.

 

[nitewulf]

does it bother anyone else that this isn't e&m?

heh...i was gonna say but...