We know the position as a function of time for an object moving in uniform circular motion is given by ~r = rcos (bt)ˆi + rsin (bt)ˆj where r and b are positive constants. we can turn this interesting 2-d motion into an interesting 3-d motion: a helical/spiral trajectory.

a) make a simple modification to the equation provided above such that the
object’s trajectory traces out a helix of fixed radius that is normal/perpendicular
to the xy−plane. justify your modification in a sentence or so.

b) based on other problems you’ve worked on this set you should be able
to modify the equation so the the helix is no longer of fixed radius, but gets
smaller and smaller or larger and larger. write down a relationship that
does this, justifying anything you add to your answer from a).

c) what would happen if we instead have ~r = rcos (at)ˆi +rsin (bt)ˆj, where
a is a new constant?

Fft review: linspace, fs, fftshift, nfft 1. generate one second of a cosine of w,-10hz sampled at f, = 100hz and assign it to x. define a tt as your time axis 2. take 64 points fft. 3. as you remember, the dft (which the fft implements) computes n samples of s2t where k-0,1,2, n -1. plot the magnitude of this 64-points fft at range 0 to 63, what do you think of this graph? 4â·to get the x-axis into a hz-frequency form, plot this 64-points fft between-50 to 50 (the 100hz sampling rate) and have n-points between them. 5. according to your figure, what frequency is this cosine wave at? 6. remember that the fft is evaluating from 0 to 2ď€. we are used to viewing graphs from-ď€ to ď€. therefore, you need to shift your graph. 7. now according to your shifted graph. what frequency is this at? 8. note that the spikes have long drop-offs? try a 1024-point dft. note that the peak is closer to 10 and the drop-off is quicker. although, now sidelobes are an issue

The boy of mass 30 kg is at r1= 2 meters from the fulcrum. of the girl is 45 kg, at what r2 must she sit so that they are balanced ?

Which magnetic property best describes a magnet’s ability to act at a distance? magnets are dipolar. magnets attract only certain objects. magnets have magnetic fields. magnets can transfer their properties to certain materials.