A particle of mass m is suspended from a support by a light string of length which passes through a small hole below the support (see diagram below). The particle moves in a vertical plane with the string taut. The support moves vertically and its upward displacement (measured from the ring) is given by a function z = h(t). The effect of this motion is that the string-particle system behaves like a simple pendulum whose length varies in time. TH z=h(t) [Expect to use a few lines to answer these questions.] a) Write down the Lagrangian of the system. b) Derive the Euler-Lagrange equations. c) Compute the Hamiltonian. Is it conserved?
A particle of mass m is suspended from a support by a light string of length which passes through a small hole below the support (see diagram below). The particle moves in a vertical plane with the string taut. The support moves vertically and its upward displacement (measured from the ring) is given by a function z = h(t). The effect of this motion is that the string-particle system behaves like a simple pendulum whose length varies in time. TH z=h(t) [Expect to use a few lines to answer these questions.] a) Write down the Lagrangian of the system. b) Derive the Euler-Lagrange equations. c) Compute the Hamiltonian. Is it conserved?
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![A particle of mass m is suspended from a support by a light string of length which passes
through a small hole below the support (see diagram below). The particle moves in a vertical
plane with the string taut. The support moves vertically and its upward displacement (measured
from the ring) is given by a function z = h(t). The effect of this motion is that the string-particle
system behaves like a simple pendulum whose length varies in time.
I
[Expect to use a few lines to answer these questions.]
a) Write down the Lagrangian of the system.
b) Derive the Euler-Lagrange equations.
z=h(t)
c) Compute the Hamiltonian. Is it conserved?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b7af157-3088-4e07-9322-eb6941ca83f4%2F3de94575-157f-40b5-bcec-f21918e2a085%2F80qixoe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A particle of mass m is suspended from a support by a light string of length which passes
through a small hole below the support (see diagram below). The particle moves in a vertical
plane with the string taut. The support moves vertically and its upward displacement (measured
from the ring) is given by a function z = h(t). The effect of this motion is that the string-particle
system behaves like a simple pendulum whose length varies in time.
I
[Expect to use a few lines to answer these questions.]
a) Write down the Lagrangian of the system.
b) Derive the Euler-Lagrange equations.
z=h(t)
c) Compute the Hamiltonian. Is it conserved?
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