Homework 3:
Simple harmonic motion, Due Sept. 14, 11:30 am
Name
.1
A 500g block is placed on a level, frictionless surface and attached to an ideal spring.
At
t
= 0 the
block moves through the equilibrium position with speed
v
o
in the –
x
direction, as shown below.
At
t
=
π
sec, the block reaches its maximum displacement of 40 cm to the left of equilibrium.
.a
Determine the value of each of the
following quantities.
Show all work.
•
period:
•
spring constant:
.b
Using
x(t)
=
A
cos
(
ϖ
t
+
φ
o
)
as the solution to the differential equation of motion:
•
Determine the form of the function
v
(t)
that represents the
velocity
of the block.
•
Evaluate all constant parameters
(A,
ϖ
,
and
φ
o
)
so as to completely describe both the position
and velocity of the block as functions of time.
.c
Consider the following statement about the situation described above.
"It takes the first
π
seconds for the block to travel 40 cm, so the initial speed
v
o
can be
found by dividing 40 cm by
π
seconds."
Do you agree or disagree with this statement?
If so, explain why you agree.
If not, explain
why you disagree and calculate the initial speed
v
o
of the block.
40 cm
t
= 0 sec:
At equilibrium
position
t
=
π
sec:
At maximum
displacement
500 g
+
x
v
o
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Homework:
Simple harmonic motion
.2
A simple pendulum consists of a particle of mass
m
suspended by a long, massless wire of length
L.
(
Note:
Neglect all frictional effects.)
.a
Draw a freebody diagram for the pendulum bob corresponding to a moment when the bob
is located an angular displacement
φ
away from (
e.g.,
to the right of) equilibrium.
.b
Determine an expression (in terms of
m, g,
and
φ
) for the component of the net force on the
bob that points tangent to the path of the bob.
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 Fall '08
 Jones,M
 Force, Friction, Mass, Simple Harmonic Motion, Work, Robert Hooke

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