Question
In: Advanced Math
A mass on a spring is subjected to an external force that looks like a triangular...
A mass on a spring is subjected to an external force that looks like a triangular wave:
F(t) = 1+t from t=-1 to 0
F(t) = 1-t from t=0 to t=1 Periodicity = 2
The differential equation for the position of the mass (using Newton’s law) ends up being: x’’(t) + 2x’(t) + 101x(t) = F(t)
1. Find the generic homogeneous solution
2. Find the Fourier series of F(t)
3. Find the Fourier series of the particular solution (which is the total solution after a long time)
4. Plot the first 5 terms of the series
Solutions
Colby Messinger answered 2 years agoRelated Solutions
Give an example of a real-world system that looks nothing like a mass on a spring...
Give an example of a real-world system that looks nothing like a
mass on a spring but still behaves like a harmonic oscillator. The
weirder the better!
can you please explain the example as well
A mass 7kg of stretches a spring 18cm. The mass is acted on by an external...
A mass 7kg of stretches a spring 18cm. The mass is acted on by
an external force of 5sin(t/2) N and moves in a medium that imparts
a viscous force of 4N when the speed of the mass is 8cm/s. If the
mass is set in motion from its equilibrium position with an initial
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A mass m, stretches horizontally from a spring which has spring constant k, and is subjected...
A mass m, stretches horizontally from a spring which has spring
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A particle moves under constant external force F = F0 ˆi. It is also subjected to...
A particle moves under constant external force F = F0
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−CDV. How will the particle move, qualitatively
speaking? Describe in words before using equations. What will the
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forces at the final velocity you found?
Determine the response of a mass-spring system when it is subjected to a half-sine pulse of...
Determine the response of a mass-spring system when it is
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In a spring-mass-dashpot system, a force of 1 Newtons is required to stretch the spring for...
In a spring-mass-dashpot system, a force of 1 Newtons is
required to stretch the spring for .05 meters. A mass of 4 kg is
hung from the spring and also attached to a viscous damper that has
a damping constant 8 Newton-sec/m. The mass is suddenly set in
motion from its equilibrium location at t = 0 by an external force
of 8 cost Newtons with initial velocity 0 m/sec. Find the transient
solution and the steady state solution of...
A force of 400N stretches a spring 2m. A mass of 50kg is attached to the...
A force of 400N stretches a spring 2m. A mass of 50kg is
attached to the end of the spring and put in a viscous fluid with a
damping force that is 100 times the instantaneous velocity. The
mass is released from the equilibrium position with a downward
velocity of 1m/s.
(a) Determine the natural frequency of the system.
(b) Determine the level of damping in the system.
(c) Write the differential equation of motion
(d) Solve the system and...
A particle of mass 2.00 kg is attached to a spring with a force constant of...
A particle of mass 2.00 kg is attached to a spring with a force
constant of 300 N/m. It is oscillating on a horizontal frictionless
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vertically on top of the 2.00 kg object as it passes through its
equilibrium point. The two objects stick together.
(a) Does the amplitude of the vibrating system increase or
decrease as a result of the collision?
decreases
increases
no change
(b)By...
A particle of mass 4.00 kg is attached to a spring with a force constant of...
A particle of mass 4.00 kg is attached to a spring with a force
constant of 300 N/m. It is oscillating on a horizontal frictionless
surface with an amplitude of 5.00 m. A 9.00 kg object is dropped
vertically on top of the 4.00 kg object as it passes through its
equilibrium point. The two objects stick together.
a) By how much does the amplitude of the vibrating system change
as a result of collision?
b) By how much does...
An undamped spring - mass system with mass m = 2 and a spring constant k = 8 is suddenly set in motion at time t = 0 by an external force f = 5 cos 3t . Determine the position of the mass as a function of time and draw the graph .
An undamped spring - mass system with mass m = 2 and a spring constant k = 8 is suddenly set in motion at time t = 0 by an external force f = 5 cos 3t . Determine the position of the mass as a function of time and draw the graph .
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