A pendulum has a length l = 0.4m and mass of 0.5 kg. a) Find the...
A pendulum has a length l = 0.4m and mass of 0.5 kg.
a) Find the angular frequency of vibration, w, for small
displacements.
b) A friction term is now added to part A. The force of friction =
-b(dx/dt) where b = 3 Ns/m. Find the new w.
c) If the mass is displaced an initial distance of 0.02 m at t = 0
and released from rest, write an expression for x(t).
Homework Answers
1. A pendulum of length L and mass M has a spring of force constant k...
1. A pendulum of length L and mass M has a spring of force constant k connected to it at a distance I below its point of suspension, Assume that the vertical suspension is rigid and that both the vertical suspension and spring are mansless (a) What is the frequency of vibration of the system for small values of the amplitude (small 0)? (b) If the pendulum is displaced by Omar and then released from rest, what is its kinetic...
A compound pendulum is made up of a rod of length L, with mass M and...
A compound pendulum is made up of a rod of length L, with mass M and a solid sphere of radius r, with mass m (see figure below). The pendulum is pivoted about one end and released from rest from and angle of 0, (angle with the vertical). (a) Find the distance, dom, of center of mass of this pendulum from its pivot. (b) Draw a free body diagram and write down Newton's 2nd Law (for rotation) for the pendulum...
13) Find a period of oscillation of this physical pendulum. M1 = 0.5 kg , L1...
13) Find a period of oscillation of this physical pendulum. M1 = 0.5 kg , L1 = 1.00 m M2 = 1.0 kg, R2 = 20 cm, a solid disk 14). Describe the oscillation ( complete an expression x(t) for that oscillation). An object being displaced on the frictionless table to the left from equilibrium position at distance 0.3 m while it moving to the left with a speed 0.6 m/s. Coefficient of spring 100 N/m, and mass of the...
A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h bel...
A pendulum of length
L
and mass
M
has a spring of force constant
k
connected to it at a distance
h
below its point of suspension (as shown in the following figure).
Find the frequency of vibration of the system for small values of
the amplitude (small
?).
Assume that the vertical suspension of length
L
is rigid, but ignore its mass. (Use any variable or symbol stated
above along with the following as necessary:
g
and
?.)
f...
A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h bel...
A pendulum of length
L
and mass
M
has a spring of force constant
k
connected to it at a distance
h
below its point of suspension (as shown in the following figure).
Find the frequency of vibration of the system for small values of
the amplitude (small
?).
Assume that the vertical suspension of length
L
is rigid, but ignore its mass. (Use any variable or symbol stated
above along with the following as necessary:
g
and
?.)
f...
A simple pendulum (mass M and length L) is suspended from a cart of mass m...
A simple pendulum (mass M and length L) is suspended from a cart of mass m that moves freely along a horizontal track shown at right. You might find it helpful to introduce the dimensionless parameters η-m/M and wo- /g/L. a What are the normal frequencies of small oscillations of the system (0 <1)? b Find and describe the corresponding normal modes of the system. c The cart/pendulum systern is held at rest in the configuration x-0 and θ K...
A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h below its point of...
A pendulum of length L and mass M has a spring
of force constant k connected to it at a distance h below
its point of suspension (Fig. P15.59). Find the frequency of
vibration of the system for small values of the amplitude (small
). Assume the
vertical suspension of length L is rigid, but ignore its
mass.
A plane pendulum of length L and mass m is suspended from a block of mass...
A plane pendulum of length L and mass m is suspended from a
block of mass M. The block moves without friction and is
constrained to move horizontally only (i.e. along the x axis). You
may assume all motion is confined to the xy plane. At t = 0, both
masses are at rest, the block is at
, and the pendulum has angular deflection
with respect to the y axis.
a) Using
and
as generalized coordinates, find the Lagrangian...
A simple pendulum has a mass of 0.202 kg and a length of 1.00 m. It...
A simple pendulum has a mass of 0.202 kg and a length of 1.00 m. It is displaced through an angle of 31.4° and then released. After a time, the maximum angle of swing is only 10.0°. How much energy has been lost to friction? a. 0.260 J b. 0.290 J c. 0.0301 J d. 1.00 J
A simple pendulum with mass m = 2.1 kg and length L = 2.3 m hangs...
A simple pendulum with mass m = 2.1 kg and length L = 2.3 m hangs from the ceiling. It is pulled back to an small angle of θ = 11.9° from the vertical and released at t = 0. 4)What is the angular displacement at t = 3.56 s? (give the answer as a negative angle if the angle is to the left of the vertical) 6)What is the magnitude of the radial acceleration as the pendulum passes through...
1. A pendulum of length L and mass M has a spring of force constant k connected to it at a distance I below its point of suspension, Assume that the vertical suspension is rigid and that both the vertical suspension and spring are mansless (a) What is the frequency of vibration of the system for small values of the amplitude (small 0)? (b) If the pendulum is displaced by Omar and then released from rest, what is its kinetic...
A compound pendulum is made up of a rod of length L, with mass M and a solid sphere of radius r, with mass m (see figure below). The pendulum is pivoted about one end and released from rest from and angle of 0, (angle with the vertical). (a) Find the distance, dom, of center of mass of this pendulum from its pivot. (b) Draw a free body diagram and write down Newton's 2nd Law (for rotation) for the pendulum...
13) Find a period of oscillation of this physical pendulum. M1 = 0.5 kg , L1 = 1.00 m M2 = 1.0 kg, R2 = 20 cm, a solid disk 14). Describe the oscillation ( complete an expression x(t) for that oscillation). An object being displaced on the frictionless table to the left from equilibrium position at distance 0.3 m while it moving to the left with a speed 0.6 m/s. Coefficient of spring 100 N/m, and mass of the...
A pendulum of length
L
and mass
M
has a spring of force constant
k
connected to it at a distance
h
below its point of suspension (as shown in the following figure).
Find the frequency of vibration of the system for small values of
the amplitude (small
?).
Assume that the vertical suspension of length
L
is rigid, but ignore its mass. (Use any variable or symbol stated
above along with the following as necessary:
g
and
?.)
f...
A pendulum of length
L
and mass
M
has a spring of force constant
k
connected to it at a distance
h
below its point of suspension (as shown in the following figure).
Find the frequency of vibration of the system for small values of
the amplitude (small
?).
Assume that the vertical suspension of length
L
is rigid, but ignore its mass. (Use any variable or symbol stated
above along with the following as necessary:
g
and
?.)
f...
A simple pendulum (mass M and length L) is suspended from a cart of mass m that moves freely along a horizontal track shown at right. You might find it helpful to introduce the dimensionless parameters η-m/M and wo- /g/L. a What are the normal frequencies of small oscillations of the system (0 <1)? b Find and describe the corresponding normal modes of the system. c The cart/pendulum systern is held at rest in the configuration x-0 and θ K...
A pendulum of length L and mass M has a spring
of force constant k connected to it at a distance h below
its point of suspension (Fig. P15.59). Find the frequency of
vibration of the system for small values of the amplitude (small
). Assume the
vertical suspension of length L is rigid, but ignore its
mass.
A plane pendulum of length L and mass m is suspended from a
block of mass M. The block moves without friction and is
constrained to move horizontally only (i.e. along the x axis). You
may assume all motion is confined to the xy plane. At t = 0, both
masses are at rest, the block is at
, and the pendulum has angular deflection
with respect to the y axis.
a) Using
and
as generalized coordinates, find the Lagrangian...
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