SCalcET8 3.3.029.
$$
θcos
(
θ
)+
sin
(
θ
)
$$2
cos
(
θ
)−
θsin
(
θ
)
If
H
(
θ
) =
θ
sin
(
θ
), find
H'
(
θ
) and
H''
(
θ
).
H'
(
θ
) =
H''
(
θ
) =

6/5/2019
hw10S3.3
3/6
5.
7/7 points |
Previous Answers
SCalcET8 3.3.035.MI.
A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is
where
t
is
in seconds and
x
is in centimeters.
(a) Find the velocity and acceleration at time
t
.
(b) Find the position, velocity, and acceleration of the mass at time
t
=
5
x
(
t
) =
4 cos
(
t
),
v
(
t
) =
$$−4
sin
(
t
)
a
(
t
) =
$$−4
cos
(
t
)
x
5
π
6
π
/
6
.
=
$$−2√3
=
$$−2
=
$$2√3
In what direction is it moving at that time?
Since
<
0, the particle is moving to the
left
.
v
5
π
6
a
5
π
6
v
5
π
6

6/5/2019
hw10S3.3
6.
4/5 points |
Previous Answers
SCalcET8 3.3.038.
An object with weight
W
is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an
angle
θ
with the plane, then the magnitude of the force is
where
μ
is a constant called the
coefficient of friction
.
(a) Find the rate of change of
F
with respect to(
θ
).
(b) When is this rate of change equal to 0?

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