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CHAPTER 19
PROBLEM 19.1
A particle moves in simple harmonic motion. Knowing that the maximum velocity is 200 mm/s and the
maximum acceleration is 4 m/s2, determine the amplitude and frequency of the motion.
SOLUTION
22
ππ
n
PROBLEM 19.2
A particle moves in simple harmonic motion. Knowing that the amplitude is 15 in. and the maximum
acceleration is 15 ft/s2, determine the maximum velocity of the particle and the frequency of its motion.
SOLUTION
4.33 ft/s
m
v=
PROBLEM 19.3
Determine the amplitude and maximum acceleration of a particle which moves in simple harmonic motion
with a maximum velocity of 4 ft/s and a frequency of 6 Hz.
SOLUTION
π
PROBLEM 19.4
A 32-kg block is attached to a spring and can move without friction in a slot
as shown. The block is in its equilibrium position when it is struck by a
hammer, which imparts to the block an initial velocity of 250 mm/s.
Determine (a) the period and frequency of the resulting motion, (b) the
amplitude of the motion and the maximum acceleration of the block.
SOLUTION
(a)
3
sin( )
12 10 N/m
32 kg
mn
n
xx t
k
m
ωφ
ω
=+
×
==
π
0.324
n
τ
(b) At 0
0, 0,tx==
00
250 mm/sxv==
Thus, 00sin((0))
mn
xx
ω
φ
== +
mmn
m
PROBLEM 19.5
A 12-kg block is supported by the spring shown. If the block is moved vertically downward
from its equilibrium position and released, determine (a) the period and frequency of the
resulting motion, (b) the maximum velocity and acceleration of the block if the amplitude
of its motion is 50 mm.
SOLUTION
(a) Simple harmonic motion. sin( )
mn
xx t
ω
φ
=
+
kk
0.30781
n
τ
(b) 50 mm 0.05 m
m
x
==
PROBLEM 19.6
An instrument package A is bolted to a shaker table as shown. The
table moves vertically in simple harmonic motion at the same
frequency as the variable-speed motor which drives it. The package is
to be tested at a peak acceleration of 150 ft/s2. Knowing that the
amplitude of the shaker table is 2.3 in., determine (a) the required
speed of the motor in rpm, (b) the maximum velocity of the table.
SOLUTION
In simple harmonic motion,
2
max max
22
2.3
150 ft/s ft
12
n
n
ax
ω
ω
=
⎛⎞
=⎜⎟
⎝⎠
(b) Maximum velocity. max max
12
vx
ω
==
⎝⎠ max 5.36 ft/sv=
PROBLEM 19.7
A simple pendulum consisting of a bob attached to a cord oscillates in a vertical plane
with a period of 1.3 s. Assuming simple harmonic motion and knowing that the
maximum velocity of the bob is 0.4 m/s, determine (a) the amplitude of the motion in
degrees, (b) the maximum tangential acceleration of the bob.
SOLUTION
(a) Simple harmonic motion sin( )
22
(1.3 s)
4.8332 rad/s
mn
n
n
t
θθ ω φ
ππ
ωτ
=+
==
=
v
tm
PROBLEM 19.8
A simple pendulum consisting of a bob attached to a cord of length 800 mm
l=
oscillates in a vertical plane. Assuming simple harmonic motion and knowing that the
bob is released from rest when 6,
θ
=
° determine (a) the frequency of oscillation, (b) the
maximum velocity of the bob.
SOLUTION
(a) Frequency.
2
(9.81 m/s )
(0.8 m)
n
g
l
ω
==
3.502 rad/s
(3.502 rad/s)
22
n
n
n
f
ω
ω
ππ
=
== 0.557 Hz
n
f=
m
m
