In the coupled pendulums of Figure 1 let us write the modulation frequency as ωm =(ω0 − ω0)/2 and the average frequency

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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.

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be constant over one cycle at the
average frequency ωp to show that the energies of the masses can be
written as

2 (13.02 KiB) Viewed 37 times

b) Show that the total energy E remains constant and that
the difference in energies at any instant of time is

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c) prove that

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to thus show that the constant total
energy is completely exchanged between the two pendulums at the
beat frequency (ω0 − ω0).

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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