The motion of a body falling in a resisting medium may be described by dv mg-by dt when the retarding force is proportional to the velocity, v. Find the velocity. Evaluate the constant of integration by demanding that v(0)=0.
The motion of a body falling in a resisting medium may be described by dv mg-by dt when the retarding force is proportional to the velocity, v. Find the velocity. Evaluate the constant of integration by demanding that v(0)=0.
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Theoretical Physics
Assignment 3 (Deadline: 20 Oct 2014)
From Kirchhoff's law the current / in an RC (resistance-capacitance) circuit obeys the equation
1
-I=0.
RdI
dt C
(a) Find I(1).
(b) For a capacitance of 10,000 microfarads charged to 100 volts and discharging through a
resistance of 1 mega-ohm, find the current I for 1-0 and 1-100 seconds.
Note: The initial voltage is IR or Q/C, where Q=SI(1)dt.
The motion of a body falling in a resisting medium may be described by
dv
m=mg-bv
dt
when the retarding force is proportional to the velocity, v. Find the velocity. Evaluate the
constant of integration by demanding that v(0)=0.
Verify that
g(0)
k² + f(r)+:
V²y(r.0.9)+[k²+,
y(r.0.9)=0
is separable (in spherical polar coordinates). The function f, g and are functions only the
variables indicated; k² is a constant.
Transform our linear, second-order, differential equation
y" + P(x)y' +Q(x)y=0
h(pp)
r² sin² 0
by the substitution y=ze
for z is
= z exp[-¦ [*P(t)dt]and show that the resulting differential equation
z"+q(x)z=0
where q(x) = Q(x)- P(x)-P²(x).
Show, by means of the Wronskian, that a linear, second-order, homogeneous, differential
equation of the form
y"(x)+ P(x)y'(x)+Q(x) y(x)=0
can not have three independent solutions. (Assume a third solution and show that the Wronskian
vanishes for all .x.)
Given that one solution of
R+ R'- R=0
r
is R=r", show that Eq. (3.56) predicts a second solution, R=r™".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10862f3f-ddf0-4895-9606-064f61dc1704%2F8265089b-69b5-49a9-bc99-2ae9d0b56709%2Fq2fjslu_processed.png&w=3840&q=75)
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Theoretical Physics
Assignment 3 (Deadline: 20 Oct 2014)
From Kirchhoff's law the current / in an RC (resistance-capacitance) circuit obeys the equation
1
-I=0.
RdI
dt C
(a) Find I(1).
(b) For a capacitance of 10,000 microfarads charged to 100 volts and discharging through a
resistance of 1 mega-ohm, find the current I for 1-0 and 1-100 seconds.
Note: The initial voltage is IR or Q/C, where Q=SI(1)dt.
The motion of a body falling in a resisting medium may be described by
dv
m=mg-bv
dt
when the retarding force is proportional to the velocity, v. Find the velocity. Evaluate the
constant of integration by demanding that v(0)=0.
Verify that
g(0)
k² + f(r)+:
V²y(r.0.9)+[k²+,
y(r.0.9)=0
is separable (in spherical polar coordinates). The function f, g and are functions only the
variables indicated; k² is a constant.
Transform our linear, second-order, differential equation
y" + P(x)y' +Q(x)y=0
h(pp)
r² sin² 0
by the substitution y=ze
for z is
= z exp[-¦ [*P(t)dt]and show that the resulting differential equation
z"+q(x)z=0
where q(x) = Q(x)- P(x)-P²(x).
Show, by means of the Wronskian, that a linear, second-order, homogeneous, differential
equation of the form
y"(x)+ P(x)y'(x)+Q(x) y(x)=0
can not have three independent solutions. (Assume a third solution and show that the Wronskian
vanishes for all .x.)
Given that one solution of
R+ R'- R=0
r
is R=r", show that Eq. (3.56) predicts a second solution, R=r™".
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