ליגרת םיענ םילגו תוצלואמ תודונת 3

‫ תנודות מאולצות וגלים נעים‬- 3 ‫תרגיל‬
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‫תנודות מרוסנות במערכת חשמלית‬
:‫נתונה המערכת הבאה של סלילים וקבלים‬
.‫מצא את הזרמים בכל אחד מהסלילים‬
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‫מערכת קפיצים מאולצת‬
.
‫ על המסה השמאלית מופעל כוח‬.‫ נחות על משטח חסר חיכוך ומחוברות ע"י קפיץ ביניהן‬m ‫שתי משקולות שמסתן‬
.‫של כל מסה‬
‫הפרופורציוני למהירות‬
‫המערכת שקועה בנוזל צמיג המפעיל על כל אחת מהמסות כוח‬
.(
‫מצא את הפתרון הכללי לתנועת המסות במצב עמיד )בזמנים‬
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Parallel-plate transmission line
Show that the self-inductance of a parallel-plate transmission line (see the figure) is given by
for
alternating current as well as for steady current, as long as the wavelength is long compared with the plate
thickness . You can use the Ampere's law as your starting point and see the discussion in Sec. 4.2, Berkeley
Vol. 3.
Fig. : The driving force (not shown) provides a potential difference V(t) between the plates at z=0 and furnishes
the current I(t) which (at any instant) is going out in the +z direction onto one plate and returning in the -z
direction on the other. The dimension a is an arbitrary length along the z direction, taken to be small compared
with the wavelength of the traveling waves.
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Coupled pendulums
Consider a linear array of coupled pendulums (motion in the z direction, lengths l, masses M, springs constant K
and the equilibrium distance between the masses a) driven periodically with
at z=0 and attached to a
rigid wall at z=L. Show that if
, then
where
and
Notice that for
this becomes simply
.
.
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Irreversible impedance matching
Consider a coaxial transmission line having 50 ohm characteristic impedance which is joined to one having 100
ohm characteristic impedance.
1. How can you insert an ordinary resistor so that an incident pulse traveling from the 50 ohm line is
transmitted without generating any reflected pulse. We want to know how many ohms the resistance has,
and we want a schematic sketch showing the center conductor and outer conductor of each of the lines at
the place where they join and showing the resistors connected. (Do not worry about "distributing" the
resistor. If the wavelengths are long compared with the diameter of the cable, there is no need to
distribute the resistance.)
2. What is the size of the transmitted pulse? (Suppose a +10-volt pulse is incident.)
3. Now suppose a +10-volt pulse is sent down this line in the other direction, i.e. from the 100 ohm line to
the 50 ohm line. What happens? Find the reflected and transmitted pulse heights.
4. Next consider the problem of transmitting a pulse from the 100 ohm line to the 50 ohm line without
generating any reflection. What should be the resistance value and how should it be connected at the
place where the lines are joined? What is the pulse height transmitted if +10 volts is inkcident? What
happens now when a +10-volt pulse is incident from the 50 ohm to the 100 ohm line?