Different modes of oscillation for a pendulum
The period of a simple pendulum is not a trivial thing, and it depends on the initial conditions.
Shown here are ten different modes of oscillation for the same pendulum. The only difference is the total amount of mechanical energy in the system.
As a result, each one has a completely different period of oscillation, unlike what the small-angle approximation (as taught in high-school) would suggest. They can’t be in sync. You may see some really interesting patterns based on the delay between them in your browser.
The red graph above each pendulum represents the phase portrait for the respective mode of oscillation, with the current state marked as a blue dot. The horizontal axis represents angle (hence why it wraps around the sides) while the vertical axis represents angular velocity.
Pendulums are very interesting dynamical systems, as they are relatively simple to understand but can produce surprisingly complex results in certain cases, such as the chaotic behavior of double pendulums and the odd behavior displayed by coupled pendulums.
Astronomers pinpoint launch of ‘bullets’ in a black hole’s jet
Using observations from NASA’s RXTE satellite and the National Science Foundation’s (NSF) Very Long Baseline Array (VLBA) radio telescope, an international team of astronomers has identified the moment when a black hole in our galaxy launched superfast knots of gas into space.
Racing outward at about one-quarter the speed of light, these “bullets” of ionized gas are thought to arise from a region located just outside the black hole’s event horizon, the point beyond which nothing can escape.
The research centered on the mid-2009 outburst of a binary system known as H1743-322, located about 28,000 light-years away toward the constellation Scorpius. Discovered by NASA’s HEAO-1 satellite in 1977, the system is composed of a normal star and a black hole of modest but unknown masses.
Their orbit around each other is measured in days, which puts them so close together that the black hole pulls a continuous stream of matter from its stellar companion. The flowing gas forms a flattened accretion disk millions of miles across, several times wider than our sun, centered on the black hole. As matter swirls inward, it is compressed and heated to tens of millions of degrees, so hot that it emits X-rays.Some of the infalling matter becomes re-directed out of the accretion disk as dual, oppositely directed jets. Most of the time, the jets consist of a steady flow of particles. Occasionally, though, they morph into more powerful outflows that hurl massive gas blobs at significant fractions of the speed of light.
Above: (1) Radio imaging by the VLBA (top row), combined with simultaneous X-ray observations by NASA’s RXTE (middle), captured the transient ejection of massive gas “bullets” by the black hole binary H1743-322 during its 2009 outburst. (2) Animation of black hole system H1743-322. (3) This 327-MHz radio view of the center of our galaxy highlights the position of the black hole system H1743-322.
Fabric of the Cosmos premieres on Nov. 2nd on PBS. Via io9:
Over the next month, NOVA is going to confirm what most sci-fi enthusiasts already suspect-that everything we’ve been taught about space and time just might be total B.S. The past is not just a series of faded events, the future isn’t yet defined, and despite what science prudes say, we probably aren’t alone.
The Fabric of The Cosmos, the four-part follow up to acclaimed physicist Brian Greene’s The Elegant Universe, takes an intensely in-depth look at all we think we know—and then turns it upside down.
The Earth has variable gravity (as seen in the “lumpy” image above) that you and I can’t feel. But could the faster-than-light neutrino experiments have been doomed by omitting this? From Forbes:
In any good heist, synchronized watches are essential for determining timing, so that a precision plan can go off without a hitch. Similarly, the clocks in a speed measurement need to be synchronized to ensure that velocity is calculated correctly. The basic problem with OPERA’s calculations, Contaldi suggests, is that the clocks used to measure the neutrinos’ velocity weren’t properly synchronized.
In the case of the faster-than light measurements, the clocks were synchronized using GPS timestamps. But, argues Contaldi, that’s not good enough. That’s because the gravity on different places on the Earth isn’t constant. The gravity at the CERN site where the neutrinos left, for example, is actually slightly greater than the gravity at the OPERA detector site. As a consequence, time would appear to move more slowly at CERN from the vantage point of the OPERA detector. Failing to take this into account, Contaldi contends, means that “[t]he resulting measurement that the neutrino velocity differs from c is not only unsurprising but should be expected in their setup.”
The Hubble Space Telescope deserves its own Nobel Prize. Perhaps they should make a Nobel Prize in a Hubble Space Telescope category, and the winner will always be the Hubble Space Telescope.
One-minute lesson on Schrödinger’s cat, and wonderful, wonderful quantum mechanics.