Homework Answers
Add Answer to:
A simple pendulum (mass M and length L) is suspended from a cart of mass m...
Prob. 7.3: A simple pendulum (mass M and length L) is suspended from a cart (mass...
Prob. 7.3: A simple pendulum (mass M and length L) is suspended from a cart (mass m) that canoscillate on the end of a spring of spring constant k, as shown in the figure at right. (a) Write the Lagrangian in terms of the generalized coordinates x and ?, where x is the extension of the spring from its equilibrium length and ? is the angle of the pendulum from the vertical. Find the two Lagrange equations. (b) Simplify the...
There is a double-pendulum system, each with mass m and length L, attached to a cart of mass M. T...
There is a double-pendulum system, each with mass m and length L, attached to a cart of mass M. The cart has linear position x, pendulum 1 has angular position θ, and pendulum 2 has angular position φ. The cart has a force, F, applied in the x-direction to the cart. m,L Using sum of forces, sum of moments, and constraint equations, determine the 12 equations 12 unknowns. Solve the system of equations for the 12 unknowns including the EOMs....
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 pendulum consists of a mass m suspended from a string of length L. When the...
A pendulum consists of a mass m suspended from a string of length L. When the pendulum is swinging, how much greater is the mass’s potential energy when the string is displaced from the vertical by the angle θ than when the mass is at the lowest position?
Q4 A ring of mass M and radius R is attached so that it can pivot asone of a rod of mass M and length 2R. the syste...
Q4 A ring of mass M and radius R is attached so that it can pivot asone of a rod of mass M and length 2R. the system is suspended by a pin at the other end of the rod and all in a uniform gravitational field,g; thus forming a double pendulum. The motion is restricted to a plane A) Show that the kinetic energy and potential energy can be written for small oscillations as: B) Find the natural frequencies...
(a) Consider a pendulum with a mass m suspended at the end of a light string...
(a) Consider a pendulum with a mass m suspended at the end of a light string of length l. As it moves through the air the mass experiences a damping force that is proportional to its speed, with constant of proportionality y. (i) Show that the angle θ that the string makes with the vertical is governed by the ordinary differential equation dt2 m dt l in the limit of small θ. 1) State the natural frequency wo of the...
(25 points) anchored to two facing walls as shown in the figure. Inside the cart, a pendulum of mass m (not included in the mass M of the cart) and length l is hung from the ceiling, z is the dis...
(25 points) anchored to two facing walls as shown in the figure. Inside the cart, a pendulum of mass m (not included in the mass M of the cart) and length l is hung from the ceiling, z is the displacement of the cart from its equilibrium position, and ф is the angle the pendulum makes with the vertical. 4. Coupled oscillators. A cart of mass M when empty is attached to two springs (a) Write down the kinetic and...
9. 25 pts] A pendulum of mass m suspended from a string of length L has...
9. 25 pts] A pendulum of mass m suspended from a string of length L has initial displacement and is released from rest. A. Write an equation for the pendulum's angular displacement as a function of time in terms of known variables. Describe how you arrived at your answer B. Sketch a qualitatively accurate graph of the pendulum's translational velocity vs time Label your scale in terms of the given quantities, and label your axes C. You make a second...
A simple pendulum consists of a ball of mass M hanging from a uniform string of...
A simple pendulum consists of a ball of mass M hanging from a uniform string of mass m and length L, with m << M. (a) If the period of oscillations for the pendulum is T, derive an expression for the speed of a transverse wave in the string when the pendulum hangs at rest in terms of m, M, T and g (the acceleration due to gravity). Your expression should not include L. (b) If the string is made...
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. 1)What is the period of oscillation? 2)What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? 3)What is the maximum speed of the pendulum? 5)What is the magnitude of the tangential acceleration as...
Prob. 7.3: A simple pendulum (mass M and length L) is suspended from a cart (mass m) that canoscillate on the end of a spring of spring constant k, as shown in the figure at right. (a) Write the Lagrangian in terms of the generalized coordinates x and ?, where x is the extension of the spring from its equilibrium length and ? is the angle of the pendulum from the vertical. Find the two Lagrange equations. (b) Simplify the...
There is a double-pendulum system, each with mass m and length L, attached to a cart of mass M. The cart has linear position x, pendulum 1 has angular position θ, and pendulum 2 has angular position φ. The cart has a force, F, applied in the x-direction to the cart. m,L Using sum of forces, sum of moments, and constraint equations, determine the 12 equations 12 unknowns. Solve the system of equations for the 12 unknowns including the EOMs....
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...
Q4 A ring of mass M and radius R is attached so that it can pivot asone of a rod of mass M and length 2R. the system is suspended by a pin at the other end of the rod and all in a uniform gravitational field,g; thus forming a double pendulum. The motion is restricted to a plane A) Show that the kinetic energy and potential energy can be written for small oscillations as: B) Find the natural frequencies...
(a) Consider a pendulum with a mass m suspended at the end of a light string of length l. As it moves through the air the mass experiences a damping force that is proportional to its speed, with constant of proportionality y. (i) Show that the angle θ that the string makes with the vertical is governed by the ordinary differential equation dt2 m dt l in the limit of small θ. 1) State the natural frequency wo of the...
(25 points) anchored to two facing walls as shown in the figure. Inside the cart, a pendulum of mass m (not included in the mass M of the cart) and length l is hung from the ceiling, z is the displacement of the cart from its equilibrium position, and ф is the angle the pendulum makes with the vertical. 4. Coupled oscillators. A cart of mass M when empty is attached to two springs (a) Write down the kinetic and...
9. 25 pts] A pendulum of mass m suspended from a string of length L has initial displacement and is released from rest. A. Write an equation for the pendulum's angular displacement as a function of time in terms of known variables. Describe how you arrived at your answer B. Sketch a qualitatively accurate graph of the pendulum's translational velocity vs time Label your scale in terms of the given quantities, and label your axes C. You make a second...
Most questions answered within 3 hours.
-
C - Language
Write a loop that sets each array element to the sum of itself...
asked 1 hour ago -
(63
#14)
which of the following statments best describes how chamging
the concentration of the substances...
asked 4 hours ago -
In the following reaction, which element is undergoing
oxidation: Na2SO3 + N2O --> N2 + Na2SO4...
asked 5 hours ago -
Which of the following pairs of ions have the same electron
configuration?
I: Br− and Se2−...
asked 8 hours ago -
The Foremost Composite Materials Company is planning a two-day
sales conference for October 19-20. The conference...
asked 8 hours ago -
3) Illustrate the observed pattern of relatedness of organisms
versus adaptations to specific conditions. This means...
asked 8 hours ago -
In winter a lake has a 0.35 m thick ice layer over 1.10 m of
water....
asked 9 hours ago -
Assuming the following has been encrypted with a Vigenere cipher
below, use the method(s) and assumptions...
asked 10 hours ago -
How would I use switch statements to write a program that will
take an input of...
asked 9 hours ago -
Imagine a reaction in which methane gas combusts at a constant
pressure of 1 atm and...
asked 10 hours ago -
Two parallel wires (each 12 m in length) are separated by a
distance of 0.065 m...
asked 10 hours ago -
Suppose there were three masses at the corner of uniform
equilateral triangle. The masses are m1...
asked 10 hours ago