The bar ABC is attached to the vertical rod with a horizontal pin. The essembly is free to rotate about the axis of the rod. in the absence of friction, the equations of motion of the system are
If the system is set into motion with the initial conditions
and
, obtain a numerical solution with the adaptive Runger-Kutta
method from
to
and plot
vs.
#!/usr/bin/env python # import numpy as np; from numpy import asarray, zeros, sin, cos, tan, pi from run_kut5 import integrate from printSoln import printSoln import pylab def cot(x): return 1./tan(x) def F(x,y): theta, theta_dot, phi, phi_dot = y # vector y is = [ theta(t), theta'(t), phi(t), phi'(t) ] F = zeros( (len(y),), dtype=float ) F[0] = theta_dot F[1] = phi_dot**2 * sin(theta) * cos(theta) F[2] = phi_dot F[3] = - 2 * theta_dot * phi_dot * cot(theta) return F x0 = 0.0 # start of the integration xStop = 1.5 # end of the integration h = 0.1 freq = 0 y0 = asarray( [ pi/12, 0, 0, 20 ], dtype=float ) X,Y = integrate(F,x0,y0,xStop,h) printSoln(X,Y,freq) if True: pylab.plot( X, Y[:,3] ) pylab.xlabel('t'); pylab.ylabel("phi'(t)") pylab.grid('on') pylab.axis('tight') pylab.show()
the above solution will give the graph and the adaptive numerical solution !
The bar ABC is attached to the vertical rod with a horizontal pin. The essembly is...
Pin P is attached to the wheel shown and slides in a slot cut in bar BD. The wheel rolls to the right without slipping with a constant angular velocity of 22 rad/s 0 140 min 200 mm Problem 15.154.a- Plane motion, velocity of a particle with respect to a rotating reference frame Knowing that x= 480 mm at θ = o", determine the angular velocity of the bar and the relative velocity of pin P with respect to the...
A block of mass m is attached by means of a spring of constant
to a wedge of mass
and height
that forms an angle
with the horizontal, as shown in the figure. Mass
can slide on the horizontal surface. Note: don't consider
friction.
a) Calculate the frequencies of small oscillations of the system
around equilibrium.
b) Find and schematically draw the relative configurations of the
normal modes corresponding to each frequency of the system.
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Part B: create an impulse momentum bar chart for the motion of
the ball with the ball and earth as the system.
You hold a beach ball with your arms extended above your head and then throw it upward. +y direction is downward We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
QUESTION 3
An L-shaped rigid bar is attached with a pivot to a wall as
shown in the figure below. Assume that the L-shaped rigid bar is
massless. A mass of m = 9.1958 kg is attached to one end
of the rigid bar and the other end is supported by spring
k = 965.7083 N/m and damper c = 121.3183 Ns/m.
Determinate the steady state amplitude of mass m,
given
where F0 =417.8427 N, ω = 48.0443 rad/s, and...
Two cylinders, each having mass m, are linked by a connecting rod whose mass is negligible. A horizontal force F(t) is applied to the right cylinder, and neither cylinder slips in its rolling motion. In the initial position, the angle θ locating the connecting pin is zero. Derive the equation of motion for this angle. We were unable to transcribe this image
Two cylinders, each having mass m, are linked by a connecting rod whose mass is negligible. A horizontal...
A mass block of mass m1 is attached to the rigid and weightless bar ABC whose other end is pin-connected to the wall The bar is supported by a spring of spring constant of k3 at its midpoint B. AB BC-a-1m. Another block of mass m2 is connected to the first block by a spring of spring constant k1 and is connected to the fixed ground by a spring of spring constant k2. The size of both blocks are ignored....
1. Springs and a mass are attached to a rigid bar, as shown in Fig 1. The hinges are free to rotate. 0 denotes the rotational angle of the rod, and 0-0 when all springs are not stretched. The mass of the bar and the size of the mass are negligible. Neglect gravitational force, and assume 0 is very small. 1) Derive the equation of motion for this system with Lagrange's method. (20pt) 2) Find the natural frequency of the...
A point mass with mass m slides on a smooth rod. The rod rotates
with a constant
around the origin on an x-y plane. Assume no external
forces.
a) Find Lagrangian of the point mass and the equation of
constraint.
b) Find Lagrange's equation of motion and eliminate the
constraint.
c) Write the Lagrange's equation with undetermined multipliers
and determine the constraint force.
We were unable to transcribe this imagem 0 = at X
(13%) Problem 3: A rod of m =
0.85 kg rests on two parallel rails that are L =
0.55 m apart. The rod carries a current going between the
rails (bottom to top in the figure, into the page) with a magnitude
I = 3.9 A. A uniform magnetic field of magnitude
B = 0.95 T pointing upward is applied to the
region, as shown in the figure. The rod moves a distance d
= 0.85 m along the...
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previous questions
In addition to the transient response charactcristics considered above, we are often interested in tho steady-state response of the system to a step reference input R(s) and constant disturbance input Ta(s) the disturbance input is used to model the friction in the motor. Pre-Lab Question 8 (3 marks) Show thal total oulput respose to the reference and disturbance inpuls n the Laplace domain is given by: (14) Tos Pre-Lab Question 9 (2 marks) What...