If: F = - k x

1
????? ?????? ??? ??????????

• ?????? ????????? ??????? (???? ???????)
• ??????? ?????? (? ??? ??????)

???? ????? ???? ????? 1- ?????? ????? ?
??????? 2- ????? ????? ?????? ??? 3- ??????? ???
?????? ????????? ???????? ?? ????? 4- ???? ???
???????? ???????? 5- ?? ??? ????????!!
2
?????? ?????? ????????? ???????
If F - k x Then, -k x m a That is, m dv/dt
m d2x/dt2 - k x d2x/dt2 (k/m) x 0 d2x/dt2
w2 x 0
w2 k/m
Or we can say, x(t) A sin (w t d)
Then, x(t) a eiwt b e-iwt Or we can say, x(t)
a sin(w t) b cos (w t)
a, b, a, b, A, d are constants that can be found
if we know enough about the problem.
3
16.4 Energy in SHM (?????? ??????? ? ??????? ??
?????? ????????? ???????)
??? ???? ????? A? ???? ?? ????? ?????? ??????
??????? ? ?????? ????????
4
16.5 An angular SHM (???? ??????? ????? ???????)
clip
t - k q
??? ??? ????? ???????
5
16.6 Pendulum (???????)
??? ?????? ??? ????? ???????? ????? ?? ?????
???????? ? ?????? ??????? ? ??????? ??????? ?
?????? (??????? ? ???????)?
??????? ??????
???? ???? ????? ?????? ?? ????? ??? ?????? ??
???????? ????
????? ???? ?????? ??????????? ?????????!!
6
16.6 Pendulum (???????)
????? ???? ?????? ??????????? ?????????!!
??????? ???????
????.. ?????? ??????? ??? ??? ??????? ? ?????
?????? ?? ???? ???????.
7
16.7 SHM and UCM (??????? ??? ?????? ?????????
??????? ? ?????? ??????????? ????????)
Nice web-site
http//webphysics.davidson.edu/physlet_resources/b
u_semester1/index.html
8
16.8 Damped (Simple) Harmonic Motion (???????
??? ?????? ????????? ??????? ?? ?????)
?? ??? ?????? ??? ????? ?????
?? ????? ?????? ??????? ?? ????? ?????? (Fd - b
v)
My Mathematica program
9
16.9 Damped (Simple) Harmonic Motion (???????
??? ?????? ????????? ??????? ?? ?????)
F Fo sin(w t)
10
?????