In Figure P4.23, assume that the cylinder rolls without slipping. The spring is at its free length when x and y are zero. (a) Derive the equation of motion in terms of x , with y t as the input. (b) Suppose that m = 10 kg, R = 0.3 m, k = 1000 N/m, and that y t is a unit-step function. Solve for x t if x 0 = x ˙ 0 = 0 .
In Figure P4.23, assume that the cylinder rolls without slipping. The spring is at its free length when x and y are zero. (a) Derive the equation of motion in terms of x , with y t as the input. (b) Suppose that m = 10 kg, R = 0.3 m, k = 1000 N/m, and that y t is a unit-step function. Solve for x t if x 0 = x ˙ 0 = 0 .
In Figure P4.23, assume that the cylinder rolls without slipping. The spring is at its free length when x and y are zero. (a) Derive the equation of motion in terms of x, with
y
t
as the input. (b) Suppose that
m
=
10
kg,
R
=
0.3
m,
k
=
1000
N/m, and that
y
t
is a unit-step function. Solve for
x
t
if
x
0
=
x
˙
0
=
0
.
PROBLEM 3.23
3.23 Under normal operating condi-
tions a motor exerts a torque of
magnitude TF at F. The shafts
are made of a steel for which
the allowable shearing stress is
82 MPa and have diameters of
dCDE=24 mm and dFGH = 20
mm. Knowing that rp = 165
mm and rg114 mm, deter-
mine the largest torque TF
which may be exerted at F.
TF
F
rG-
rp
B
CH
TE
E
1. (16%) (a) If a ductile material fails under pure torsion, please explain the failure
mode and describe the observed plane of failure.
(b) Suppose a prismatic beam is subjected to equal and opposite couples as shown
in Fig. 1. Please sketch the deformation and the stress distribution of the cross
section.
M
M
Fig. 1
(c) Describe the definition of the neutral axis.
(d) Describe the definition of the modular ratio.
using the theorem of three moments, find all the moments, I only need concise calculations with minimal explanations. The correct answers are provided at the bottom
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.