Simple harmonic motion problems

[ilovephysics]

1. three 10,000kg ore cars are held at rest on a 30degree incline on a mine railway using a cable that is parrallel to the incline. The cable is observed to strech 15cm just before the coupling between to lower two cards creaks, detaching the lowest car. Assuming the cable obeys Hook's Law. Find a) the frequency and b) the amplitude of the resulting oscillations of the two remainin cars

-for part a i tried using Fnet= -kx, Fnet being the mass of the 3 cards times gravity times ( sin30 times .15m ) and solving for k, and then puttin k into the formula f = (1/2pi)(sqrt k/m ) i don't know if this is right..
-for part b i don't know how to find the amplitude because in all the equations there are 2 uknowns and i don't know how to solve for the amplitude

4. A 2200lb car carrying four 180lb people drives over a rough "washboard" dirt road with corrugations 13ft apart. The car bounces with maximum amplitude when its speed hits 10mi/h. The car now stops and the four people get out. By how much does the car rise on its suspensions owing to this decrease in weight?

-i know we have to use the mass of the people not the weight, but i don't understand how we use all the information to find how much it rises

5. A small mass with m = 100 grams is attached to a vertical string of length l=2m in the Earth's gravity. The mass swings back and forth with no loss of energy. The maximum angle from the vertical is 45 degrees. This problem is not simple harmonic motion because the maximum angle of displacement is not small. Find the velocity when the string is vertical, theta = 0. Find the tension in the string at theta = 0. What is the velocity at theta = 0 if you assume simple harmonic motion?

-i know how to calculate the last part when we assume it is simple harmonic, but how do you find the other stuff if it ISNT SHM?

would appreciate if someone could help me, these questions seem to have me stuck, thanks

 

[ChronicQuantumAddict]

for number five u need to look at the equations of motion for an osciallator.

 

[ilovephysics]

and what are those? i only know equations for simple harmonic motion and the textbook only talks about pendulums with small amplitudes and shm

 

[maverick280857]

Thats what it is. A pendulum, a block on a spring, two blocks with a spring mediating the forces are all examples of Simple Harmonic Oscillators for small displacements obeying Hooke's Law (which states that the restoring force is proportional to the displacement). SHM means Simple Harmonic Motion, which is the motion that a simple harmonic oscillator performs under these conditions. You need to apply the same fundamental ideas for all problems where SHM takes place.

In general a motion may be oscillatory BUT NOT Simple Harmonic. This is usually when Hooke's Law breaks down or is not applicable to start with. This generally happens when the amplitude of motion is large and so the restoring force and displacement of the body performing SHM are no longer linearly related (simply put something like $F = -kx$ doesn't hold).

If you noticed, SHM is governed by equations of the form

[tex]\ddot{r} + \omega_{0}^2r = 0[/itex]

This is a ordinary second order linear differential equation with constant coefficients (if the terminology confuses you, ignore it for now). For more complicated motions where a form of Hooke's Law does not hold, the differential equations of motion are not so simple to solve and sometimes only approximate solutions can be found. In general therefore, you cannot solve them by hand as easily as you can solve SHM equations. All you can do is set up the equations of motion using the same principles. Solving them may not be always possible.

Hope that helps.

Cheers
Vivek