What is Oscillatory motion: Definition and 50 Discussions
Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.
Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy.
First of all, the problem is not clearly defined as they don't specify if the given mass is the total mass of the car, or just the sprung mass of the car, which is really what's relevant. In any case, with the limited information given, it seems like one is forced to make the assumption that...
I am a layman with very little experience in math and physics and recently I became curious about how to analyze dampened oscillations occurring in fluid mediums, such as those following a disturbance in a pool of water. What sort of math and physics is required to understand this phenomenon and...
First of all, i know that the motion will be bounded, is not necessary to know if the motion will be closed or not.
Second, by analyzing the graphic of a effective potential with such conditions, the motion will agree with harmonic motion.
Ok
I don't know how to prove the harmonic oscillation...
Here is the diagram of the problem:
and here is the answer of the question:
What I don't understand is equation 1 and 2.
The Hook's law states that F = -k(change in x)
Why the change in x1 equals to x1-x2+l? x1-x2 equals to the length of the compressed spring. I cannot convince myself that...
The fig. 1.1(a) is a mass m attached to a spring that is fixed to a wall. I don't understand what does "a sudden momentum impulse" means. Is it an external force o what?
I imagined that the new equation of motion would be
md^2x/dt^2+dp1/dt-kx=0
md^2x/dt^2+mdv1/dt-kx=0
is this the equation i...
Homework Statement
The equation y = A sin(kx - wt + pi/2) is the same as
a. y = -A sin(kx - wt + pi/2)
b. y = A cos(kx - wt)
c. y = -A cos(kx - wt)
d. y = -A sin(kx - wt - pi/2)
e. y = A sin(kx - wt + (3pi)/2)
Homework Equations
y = A sin[(2pi)/lamda * x - (2pi)/period * t + (phase constant)]...
The figure below shows a system in equillibrium. The pulley and the springs (both with constants "k") are ideal. The period of oscillation of the mass A is given by:
Relevant equations:
F = -kx (SHM)
I tried to do a "force diagram" and set up some geometric relations but it´s not working.
Homework Statement
2 masses are connected by a spring. They are on a frictionless plane inclined relative to the horizontal by ##\alpha##. The masses are free to slide, rotate about their center of mass, and oscillate.
1. Find the Lagrangian as a sum of the Lagrangian for the COM motion and a...
Homework Statement
I thought that in the situation where mass is attached to the string and put into motion (vertically), energy goes between 1/2 kA^2 and 1/2 mV^2 like here - http://imgur.com/RU4P6UW
However in student's book I saw the table, which said that potential energy of gravity is...
My textbook says, "Very often the body undergoing periodic motion has an equilibrium position somewhere inside its path."
" If a body is given a small displacement from the equilibrium position, a force comes into play which tries to bring the body back to the equilibrium point giving rise to...
A Case of Mechanical Waves
Case: Is There Any Mechanical Oscillatory System Where Maximum Velocity of Resonance Will Increase More Than Speed of the Light?”
Consider a child, who is playing with a swing. During the period of the time, he learns to apply the optimum force to the swing in order...
Can someone recommend me some good textbooks or articles that contain or focus on statistical thermodynamics and/or oscillatory motion (preferably with advanced math, not just stories)?
Relevant equations
1)
2) T = \sqrt{ \frac{m}{k} }
3) T = \frac{2 \pi }{ \omega } In some problems about damped oscillatory motion, the requests ask for example "Calculate the amplitude after 20 oscillations"
I know that i need to find the period first of all but :
Do i find the period...
Homework Statement
Which of the following is a forced frequency acting on the oscillations?
I. A pendulum skims the surface of a pool of water at the lowest point of motion.
II. To keep a bell ringing, a bell ringer pulls on a bell rope.
III. A singer shatters a glass.
Homework EquationsThe...
Homework Statement
Two masses slide freely in a horizontal frictionless track and are connected by a Spring whose force constant is k. Fid the frequency of oscillatory motion for this system.
Homework Equations
My professor posted the solution but I am having trouble understanding everything...
Homework Statement
The position of a particle is given in cm by x = 6*cos(3πt), where t is in seconds.
What is the first time that the particle is at x = 0 and moving in the +x direction?
Homework Equations
The Attempt at a Solution
I set x=0, and divided 0 by 6...
Hi, i started to learn oscillatory motion today, and my teacher didn't teach us very well...and he told us that we were to conduct a oscillatory motion lab. So, me and a couple of other friends conducted a spring not moving that was hanged vertically and just calculated the displacement of the...
Hi all
I'm from Bioengineering and unfortunately not too expert on the mechanical side. I'm making a device for which I need a mechanism to transform circular motion into oscillatory motion. I found the mechanism in the picture below...
Homework Statement
Use energy to show whether or not the data agrees with the law of conservation and explain.
Mass-.3105kg spring constant-6.412 Equailibrium position-1.082
Max positive postion (1) farthest distance to the right of the equlibrium position
time-3.70s...
Homework Statement
A particle with mass m which can move only in one dimension, is subject to a constant force
F= \begin{cases}-F_{0} && x>0\\F_{0} && x<0\end{cases} with F_{0}>0.
First I've got to say if there is a potential energy. Then i must solve the particle dynamics (i.e. find v(t)...
A 0.980kg block slides on a frictionless, horizontal surface with a speed of 1.32m/s. The block encounters an unstretched spring with a force constant of 245N/m.
(a)How far is the spring compressed before the block comes to rest?
(b) How long is the block in contact with the spring before...
Homework Statement
A particle moves in simple harmonic motion with a frequency of 3.00 oscillations/s and an
amplitude of 5.00 cm. (a) Through what total distance does the particle move during one cycle
of its motion? (b) What is its maximum speed? Where does this occur? (c) Find...
Homework Statement
This is an exercise on classical mechanics, filed under the section on oscillatory motion (according to the lecture notes).
A car is driven with constant speed 30 km/h along a bumpy road. The height of the road may be described as y = y(x) = H_0 \sin(kx), x>0. Now set...
A model of the carbon dioxide (CO2) molecule is constructed as shown in Fig. SM10.1
Two sliders A and C, each of mass M, represent the oxygen atoms and are connected by light springs, of force constant k, to a slider B of mass m, representing the carbon atom. All three sliders are placed on a...
Homework Statement
Position of particle is given by:
x(t) = 5 cos (3t +2)
At what time after t = 0 is the particle at the equilibrium position?
Homework Equations
The Attempt at a Solution
I understand the equilibrium position to be the point where x(t) = 0 since x(t) is...
Is there a quantitative relationship between dampening of a mass on a spring and time. I need some help on how to go about finding a mathematical relationship of dampening of a mass on a spring.
thank you
Homework Statement
A student measures the unstretched length of a spring as 11.2 cm. When a 100.0 g mass is hung from the end of the spring, its length is 20.7 at rest. The mass-spring system is set into oscillatory motion and the amplitude of the motion decreases to half its original value in...
Homework Statement
A 0.321-kg mass is attached to a spring with a force constant of 13.3 N/m. If the mass is displaced .256 m grom the equilibrium and released, what is its speed when it is .128 m from equilibrium. The answer is 1.43 m/s
Homework Equations
k=(w^2)m
w=2pi/T
The...
Homework Statement
A particle with a mass of 0.5 kg is attached to a horizontal spring with a force constant of 50 N/m. At the moment t = 0, the particle has a maximum speed of 20 m/s and is moving to the left.
(a) Determine the particle's equation of motion.
(b) Where in the motion is the...
Hey there,
The Question
Points A,B,C,D, and E lie in a straight line. AB=BC=15 cm, CD=10 cm and DE=20 cm. A particle is moving with SHM so that A and E are the extreme positions of its motion. The period of the motion is 0.2s. Find the time the particle takes to get from B to D
i) if it is...
Homework Statement
A mass is oscillating on a spring with a period of 4.85 s. At t = 0 the mass has zero speed and is at x = 9.90 cm. What is the magnitude of the acceleration at t = 1.40 s?
Homework Equations
a=-w2x
x(t)=Acos(wt+phi)
The Attempt at a Solution
I tried using the...
Homework Statement
A mass m is suspended on a vertical spring. The mass is released from the equilibrium position of the spring without the mass. Find the position of the mass as a function of time, while neglecting friction.
Homework Equations
ma=-kx + mg
The Attempt at a Solution...
Homework Statement
mass of A=5,0kg
mass of B=2,0kg
friction coefficient between A and the plan=0,30
The system is moving with an acceleration of 7,5 m /s^2 and the angle theta is constant and equals to 37º.
Then, a mechanism makes the body A and the body B stops. B stop when it is in...
"Resonance in an un-damped spring-mass system"
If I have a force that is pushing upwards on a spring-mass system, and I basically have to find an equation that will give me the velocity and y-position for any given t, how much does that differ from the general form of Asin (\omegat +\phi)...
Hi,
I have been working on the solution to a damped, sinusoidally driven system and their electric-circuit analogs. I can break the equation of motion into the homogeneous and particular portions, and understand that x(t) is the sum of the two solutions. I also understand that the...
Homework Statement
1. A screw is put into the top of a coconut and a long string is tied to the coconut so that it can be suspended to form a simple pendulum. A hole is then punched into the bottom of the coconut and the system is made to oscillate. The period of this pendulum is found to...
Homework Statement
The amplitude of the oscillation gradually increases till block B starts to slip. At what A does this happen?(there is no friction between the large block and the surface)
Homework Equations
Force equations etc... (F=ma) and
I reckon it has something to do...
Homework Statement
The moment of inertia for an arm or leg can be expressed as I = amL2, where a is a unitless number that depends on the axis of rotation and the geometry of the limb and L is the distance to the center of mass. Say that a person has arms that are 27.80 cm in length and legs...
A 2.25-g bullet embeds itself in a 1.50-kg block, which is attached to a spring of force constant 785 N/m. If the maximum compression of the spring is 5.88cm find (a) the initial speed of the bullet and (b) the tie for the bullet-block system to come to rest
I used:
E = K + U =...
Hi everyone,
Could someone please help me with the fundamentals of oscillatory motion.
A 1 metre ruler is suspended on both ends by two strings attatched to retort stands. The length of the string is increased to observe the increase in period of oscillation.
I need to know the...
Hello all,
Any help with this will be much appreciated. I've scoured the web and searched through textbooks, but I don't have a definite answer to my question as of yet.
First, here's the background on my question:
If I have a standard mass on a spring set into motion, All the textbooks...
Homework Statement
Four people, each with mass of 71.3 kg, are in a car with a mass of 1130 kg. An earthquake strikes. The vertical oscillations of the ground surface make the car bounce up and down on its suspension springs, but the driver manages to pull off the road and stop. When the...
A Mass is oscillating on a spring, with a normal equation of motion being:
x(t) = xmax sin(wt)
Were also given that the energy equation is E = 0.5mv^2 + 0.5mw^2 x^2
Now, we need to find the probability P(x,deltax) of finding the mass in a small region of size delta x.
I really have no idea...
There is a displacement versus time graph of a 3.4 g mass on a spring that is in oscillatory motion. A=0.5 and the wavelength for one period is 3 s while the total time shown on the graph is 7 s. I need to find out the maximum speed of this mass.
At first I thought that it would easily be...
I'm having some trouble with oscillatory motion...
"A transverse wave on a string is described by the equation
y(x, t) = (0.350 m)sin [(1.25 rad/m)x + (99.6 rad/s)t]
Consider the element of the string at x = 0. (a) What is the time interval between the first two instants when this element...
1.) A cube 1.50 cm on edge mounted on the end of strip that lies in vertical plane. Mass of strip is neglible, but the length of the strip is much larger than cube. The other end of strip is clamped on to a stationary frame. A horizontal force of 1.43 N applied to the cube is required to hold it...
Hey can someone guide me in the right direction here.
Q. Show that the time rate of change of mechanical energy for a damped , ubdriven oscillator is given by dE/dt=-bv^2 and hence is always negative.
Proceed as follows: Differentiate the expression for the mechanical energy of an...
I've got a test coming up with a problem similar to this one, I've figured out some of it but I am kinda lost on the rest, here it goes:
A solid sphere (radius = R) rolls without slipping in a cylindrical trough (radius = 5R). Show that, for small displacements from equilibrium perpendicular...