Superimposed Simple Harmonic Motions: Resultant Time Period Analysis

[the_terminator]

what is the resultant time period when two simple harmonic motions of time periods 3s and 4s superimpose

 

[berkeman]

Try making an Excel plot to see what happens when you add two sine waves like that. BTW, "resultant time period" is not a precise term -- the original question probably asked for the period of the waveform or something? When you add sound waves of two different frequencies, for example, you get what are called "beats" where the superposition sound gets louder and softer at a specific rate. That may be what the question is asking for you to figure out -- what is the period of the beats when you add these two signals...

 

[row]

i think it may be solved this way but not sure if it is right,
let y=Asin(wt+θ) for T=3
and Y=Asin(wt)for T=4 in 1 sec, Y shm reaches an extreme,this implies that
at the other extreme it reaches at t=3 sec (by symmetry)
ie.the shm y completed 1 ossicilation
hence phase diff. of ∏/2
hence although T is not vector one can always relate it to velocity or acc.
hence resultant T=√(3²+4²)=5

ps.do you have the solutions?

 

[berkeman]

I didn't understand Row's solution, but maybe a little plot from Mathematica will help the OP:

Plot[{Sin[2 Pi t/3] + 2.5, Sin[2 Pi t/4] + 2.5,
Sin[2 Pi t/3] + Sin[2 Pi t/4]}, {t, 0, 20}, PlotRange -> {-2.5, 5}]

 

[row]

yep that was a silly thing i guess, so time period cannot be added as vectors
but when you look at the graph,doesnt it seem as 12.
so can we argue that they are the LCM??