1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: SHOW: if x1 & x2 have a period T then x3 = a*x1 + b*x2 also has period T

  1. Sep 6, 2007 #1
    1. The problem statement, all variables and given/known data

    Show that if [itex]x_1(t)[/itex] and [itex]x_2(t)[/itex] have period T, then [itex]x_3(t)\,=\,ax_1(t)\,+\,bx_2(t)[/itex] (a, b constant) has the same period T.

    2. Relevant equations



    3. The attempt at a solution



    Since the relevant equations (above) are true...




    Does this look right?
  2. jcsd
  3. Sep 6, 2007 #2


    User Avatar
    Science Advisor

    Yes, that's fine. That shows that if T is a period of both x1 and x2 then it is a period of ax1+ bx2 for any a and b. It is NOT always true that if T is the period (i.e. smallest period) of both x1 and x2 then it is the period of ax1+ bx2. Example: x1= sin(x)+ sin(2x), x2= -sin(x)+ sin(2x). Then [itex]2\pi[/itex] is the period of both x1 and x2 but x1-x2= 2sin(2x) which has fundamental period [itex]\pi[/itex]. (But [itex]2\pi[/itex] is still a period.)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook