Question
In: Advanced Math
The motion of a mass-spring system with damping is governed by y''(t) + by'(t) + 64...
The motion of a mass-spring system with damping is governed by y''(t) + by'(t) + 64 y(t) = 0; y(0) = 3, and y'(0) = 0.
Find the equation of motion for b = 0,14,16, and 20.
.
Solutions
Colby Messinger answered 1 week agoRelated Solutions
Suppose that the mass in a mass-spring-dashpot system with m = 10, the damping constant c...
Suppose that the mass in a mass-spring-dashpot system with m =
10, the damping constant c = 9, and the spring constant k = 2 is
set in motion with x(0) = -1/2 and x'(0) = -1/4.
(a) Find the position function x(t).
(b) Determine whether the mass passes through its equilibrium
position. Sketch the graph of x(t).
Consider an mass-spring system with the following IVP for its disagreement y (t) at time t...
Consider an mass-spring system with the following IVP for its
disagreement y (t) at time t greater than or equal to 0. You may
assume it is underdamped.
y" + y' + 5y = 0 , y (0) = -2 , y '(0) = -1
(a) Convert this to a DE system IVP in displacement y and
velocity v.
(b) Without using technology or solving the second order DE,
make a rough sketch of the system solution on a phase...
1) Sinusoidal Motion Properties in Spring Mass System- A 200g mass hangs from vibrating spring at...
1) Sinusoidal Motion Properties in Spring Mass System- A 200g
mass hangs from vibrating spring at lowest point of 3cm above table
and at it's highest point at 12cm above table. It's oscillation
period is 4seconds. Determine the following:
a. The spring constant in terms of T (period)
b. The maximum velocity magnitude and maximum acceleration
magnitude
c. The velocity magnitude at 10cm above table
d. The vertical position, velocity magnitude and acceleration
magnitude at 5 seconds
How is the motion of the mass on the spring similar to the motion of the...
How is the motion of the mass on the spring similar to the
motion of the bob? How is it different? Then, why does the period
of a pendulum not depend on mass but it does for the spring?
Explain carefully. Simple harmonic motion is used to describe
physics most complex theories. How could something so simple
describe the most complex
A mass on a spring undergoes simple harmonic motion. At t = 0 its displacement is...
A mass on a spring undergoes simple harmonic motion. At t = 0
its displacement is 1m and its velocity is 1m/s towards the
equilibrium position. What single piece of information allows you
to determine frequency and amplitude?
A. mass
B. spring constant (k)
C. kinetic energy at t = 0
D. acceleration at t = 0
E. force at t = 0
A spring with a mass of 1 kg has damping constant 10 kg/s and a spring...
A spring with a mass of 1 kg has damping constant 10 kg/s and a
spring constant 41 kg/s2 . If the spring begins at equilibrium
position and is given a velocity of 2 m/s, find the position of the
mass at any time t. Is this overdamping, critical damping or
underdamping?
A spring with a mass of 1 kg has damping constant 10 kg/s and a spring...
A spring with a mass of 1 kg has damping constant 10 kg/s and a
spring constant 41 kg/s2 . If the spring begins at equilibrium
position and is given a velocity of 2 m/s, find the position of the
mass at any time t. Is this overdamping, critical damping or
underdamping?
The Equation of motion for the standard mass-spring-damper system is Mẍ + Bẋ + Kx =...
The Equation of motion for the standard mass-spring-damper
system is
Mẍ + Bẋ + Kx = f(t).
Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m},
determine the free response of the system to initial conditions {
x0 = -1m, v0 = 40 m/s}. To help verify the
correctness of your answer, a plot of x(t) should go through the
coordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03,
-0.2043}.
Numerically simulate the...
The Equation of motion for the standard mass-spring-damper system is Mẍ + Bẋ + Kx =...
The Equation of motion for the standard mass-spring-damper
system is
Mẍ + Bẋ + Kx = f(t).
Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m},
determine the free response of the system to initial conditions {
x0 = -1m, v0 = 40 m/s}. To help verify the
correctness of your answer, a plot of x(t) should go through the
coordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03,
-0.2043}.
Numerically simulate the...
The Equation of motion for the standard mass-spring-damper system is Mẍ + Bẋ + Kx =...
The Equation of motion for the standard mass-spring-damper
system is
Mẍ + Bẋ + Kx = f(t).
Given the parameters {M = 2kg, B = 67.882 N-s/m, K = 400 N/m},
determine the free response of the system to initial conditions {
x0 = -1m, v0 = 40 m/s}. To help verify the
correctness of your answer, a plot of x(t) should go through the
coordinates {t, x(t)} = {.015, -0.5141} and {t, x(t)} = 0.03,
-0.2043}.
determine the steady-state...
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