Two blocks and three springs are configured as shown in the figure. All motion is horizontal. When the blocks are at rest, all springs are unstretched. kiz kiz ee m1 ell m2 ] Choose as generalized coordinates the displacement of each block a. . from its equilibrium position and write the Lagrangian. b. . ] Find the T and V.
Two blocks and three springs are configured as shown in the figure. All motion is horizontal. When the blocks are at rest, all springs are unstretched. kiz kiz ee m1 ell m2 ] Choose as generalized coordinates the displacement of each block a. . from its equilibrium position and write the Lagrangian. b. . ] Find the T and V.
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![Two blocks and three springs are configured as shown in the figure. All motion is
horizontal. When the blocks are at rest, all springs are unstretched.
6.
k1
kiz
ell
m1
m2
a. . ] Choose as generalized coordinates the displacement of each block
from its equilibrium position and write the Lagrangian.
b. .
c. :.
-] Find the T and V.
] Suppose
m, = 2m,
k, = 4k,
m2 = m,
k2 = k,
kz = 2k
Find the frequencies of small oscillations.
d.
-] Find the normal modes of oscillation.
..] At time t = 0, mass #1 is displaced by a distance b relative to its
equilibrium position. i.e. x, (0) = b. The other initial conditions are x,(0) = 0,
*1(0) = 0, and xz(0) = 0. Find t , the next time at which x2 vanishes.
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Transcribed Image Text:Two blocks and three springs are configured as shown in the figure. All motion is
horizontal. When the blocks are at rest, all springs are unstretched.
6.
k1
kiz
ell
m1
m2
a. . ] Choose as generalized coordinates the displacement of each block
from its equilibrium position and write the Lagrangian.
b. .
c. :.
-] Find the T and V.
] Suppose
m, = 2m,
k, = 4k,
m2 = m,
k2 = k,
kz = 2k
Find the frequencies of small oscillations.
d.
-] Find the normal modes of oscillation.
..] At time t = 0, mass #1 is displaced by a distance b relative to its
equilibrium position. i.e. x, (0) = b. The other initial conditions are x,(0) = 0,
*1(0) = 0, and xz(0) = 0. Find t , the next time at which x2 vanishes.
е.
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