In the coupled pendulums of Figure 1 let us write the modulation frequency as ωm =(ω0 − ω0)/2 and the average frequency
Posted: Wed May 18, 2022 4:37 pm
In the coupled pendulums of Figure 1 let us write the modulation
frequency as ωm =(ω0 − ω0)/2 and the average frequency as ωp = (ω0
+ ω0)/2 and suppose that the spring is so weak that it stores a
negligible amount of energy.
a) Let the modulated amplitude.
be constant over one cycle at the
average frequency ωp to show that the energies of the masses can be
written as
b) Show that the total energy E remains constant and that
the difference in energies at any instant of time is
c) prove that
to thus show that the constant total
energy is completely exchanged between the two pendulums at the
beat frequency (ω0 − ω0).
Ao cos(wmt) ó Ao sen(wmt)
1 ΕΙ II 5mAĞw cos? (wmt) , 5mAwsen"(wmt). 2 1 E2
. [t( ولما - أنا)]E1 - E2 = E cos
Ei E12R2 号 [1+cos(u' - un) [1-cos(L. - up)]. E2
Qo0000000000000 elle 20000000000 444 Г. III
frequency as ωm =(ω0 − ω0)/2 and the average frequency as ωp = (ω0
+ ω0)/2 and suppose that the spring is so weak that it stores a
negligible amount of energy.
a) Let the modulated amplitude.
- 1 (9.43 KiB) Viewed 39 times
average frequency ωp to show that the energies of the masses can be
written as
- 2 (13.02 KiB) Viewed 39 times
the difference in energies at any instant of time is
- 3 (8.22 KiB) Viewed 39 times
- 4 (17.52 KiB) Viewed 39 times
energy is completely exchanged between the two pendulums at the
beat frequency (ω0 − ω0).
- 5 (31.43 KiB) Viewed 39 times
1 ΕΙ II 5mAĞw cos? (wmt) , 5mAwsen"(wmt). 2 1 E2
. [t( ولما - أنا)]E1 - E2 = E cos
Ei E12R2 号 [1+cos(u' - un) [1-cos(L. - up)]. E2
Qo0000000000000 elle 20000000000 444 Г. III