What is Periodic motion: Definition and 28 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.
TL;DR Summary: Prove that a sum of trigonometric ratios is periodic but not not simple harmonic.
We need to prove that ##x = sin{\omega t} + sin{2\omega t} + sin{4\omega t}## where ##x## is the displacement from the equilibrium position at time ##t##.
I can see that each term is a SHM, but...
Homework Statement
A thin 0.50-kg ring of radius R = 0.60 m hangs vertically from a horizontal knife-edge pivot about which the ring can oscillate freely.
If the amplitude of the motion is kept small, what is the period?
Homework Equations
T = 2pi / ω
Not sure what others...
The Attempt...
Homework Statement
"Each piston of an engine makes a sharp sound every other revolution of the engine. (a) How fast is a race car going if its eight-cylinder engine emits a sound of frequency 750 Hz, given that the engine makes 2000 revolutions per kilometer? (b) At how many revolutions per...
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...
Homework Statement
Identical ropes were tied to two trees, and two men, A and B, started shaking the free ends at the same instant a short while ago (Figure 1) .
Which rope has the greater tension?
Which man is shaking with the greater frequency?
Homework Equations
T=1/f λf=v
The Attempt...
Homework Statement
Please see the attached.I don't know how to do (ai).
potential function is the potential energy defined by f = -dV/dx
e is the total energy of the system where
e = KE + PE
= (dx/dt)^2 /2 + V
Note:m=1 because the particle has a unit mass
If you integrate f,you get V(the...
Homework Statement
A pendulum with a mass of 0.1 kg was released. The string made an angle of 7 ° with the vertical. The bob of the pendulum returns to its lowest point every 0.1 seconds.
What is the period, frequency?
Homework Equations
T= 1/f
T=sec/cycles
F= cycles/sec
The Attempt at a...
1. According to physicsclassroom.com, periodic motion is defined as "a motion that is regular and repeating." But the example included does not factor in damping (it's assumed that there's no air resistance and the spring will keep vibrating for eternity.)...
Homework Statement
Planet 1 orbits Star 1 and Planet 2 orbits Star 2 in circular orbits of the same radius. However, the orbital period of Planet 1 is longer than the orbital period of Planet 2. What could explain this?
A) Star 1 has less mass than Star2.
B) Star 1 has more mass than Star 2
C)...
Homework Statement
A block os mass m is attached to a horizontal spring, which is attached to a wall. The block is oscillating without friction with initiation amplitude A0 and maximum velocity v0. When the block is at its maximum amplitude (and therefore instantaneously at rest), is it struck...
Homework Statement
Four weightless rods of length ##l## each are connected by hinged joints and form a rhomb (Fig. 48). A hinge A is fixed, and a load is suspended to a hinge C. Hinges D and B are connected by a weightless spring of length ##1.5l## in the undeformed state. In equilibrium, the...
I am having difficulties writing my damped oscillations lab report. We were asked to write a short essay on eddy currents (creation,direction advantage and disadvantage) and their relationship with torsion pendulums. Also,we have to explain if the copper wheel in the torsion pendulum could be...
Homework Statement
A mass m = 2.0 kg is attached to a spring having a force constant k = 990 N/m as in the figure. The mass is displaced from its equilibrium position and released. Its frequency of oscillation (in Hz) is approximately _____ . [/B]
Homework Equations...
In lecture, we are beginning to learn about waves and periodic motion under simple harmonic motion. We were given the equations:
x=Acosθ and θ=ωt+\phi -- Substituting, we get x=Acos(ωt+\phi).
This is simple enough; however what is Phi? All I was told is that "phi is a constant that allows us...
Homework Statement
Consider a spring hung vertically from the ceiling.
a) When a 2kg mass is attached to the spring, the spring is stretched 0.10m. What is the force constant of the spring?
b) The 2kg mass is removed and a different one attached to the spring. It then undergoes simple...
Please help with periodic motion problems!
1. What are the correct units for frequency? What are the correct units for angular frequency?
2. A grandfather clock keeps time by using a pendulum. If you want to design a pendulum to have a period of 1 s, estimate how long you should make the...
According to our textbook "..every periodic motion, however complicated it may be, can always be resolved into simple oscillatory components." Can someone explain this? How can the periodic motion of Earth be resolved into oscillatory components?
Homework Statement
By direct substitution, show that equation (3) is a solution of the differential equation (2).
Homework Equations
(2) (d^2 θ)/(dt^2 )=-g/l θ (Second derivative of θ(t)=-g/l θ.)
(3) θ(t)=θ_0 cos(√(g/l) t)
The Attempt at a Solution
I...
Homework Statement
A 1.50-kg, horizontal, uniform tray is attached to a vertical ideal spring of force constant 185 N/m and a 275-g metal ball is in the tray. The spring is below the tray, so it can oscillate up-and-down. The tray is then pushed down 15.0 cm below its equilibrium point (call...
Three parallel, infinite, uniformly charged planes are arranged as shown in Figure 24.32.
(it looks just like it's described. The middle plate is positive sigma, the outer plates are both negative sigma.)
Homework Statement
A small hole passes through the middle plane. At t=0 an...
i have two questions from kleppner's book, here it goes (iv'e attached a file which have the sketchs of the two problems):
6.17
A rod of length l and mass m, pivoted at one end, is held by a spring at its midpoint and a spring at its far end, both pulling in opposite directions.
The springs...
I am working on a problem that has a few angles of approach. I am hoping to get at least that right before I waste too much more time. The problem is a slender, uniform, rigid rod is placed to pivot on its center, so that the rotation is taking place at the ends of the rod.
then a spring...
Hi. I am currently working on a problem involving a ball being dropped from a hieght of 4m making a perfectly elastic collision with the ground. Assuming no mechanical energy is lost due to air resistance, I must find the period of the motion.
I used the equation
V(final) = V(initial) - gt...
Here is my problem:
A hard-boiled egg of mass 45.0 g moves on the end of a spring with force constant k = 24.7 N/m. Its initial displacement is 0.290 m. A damping force F = - bv acts on the egg, and the amplitude of the motion decreases to 0.120 m in a time of 5.10 s.
I need to find the...