Period Definition and 1000 Threads

I have a question concerning the eccentricity vs orbital period of observed exoplanets. Going to this link let's you plot different exoplanet properties on each axis of a graph. Plugging in Orbital Period for the X-axis and Eccentricity for the Y-axis shows that a trend towards decreasing...

Homework Statement If there were a planet three times farther from the sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun? Assume the orbit is a circle. Homework Equations Kepler's 3rd Law ##= (\frac{r_1}{r_2})^3 = (\frac{T_1}{T_2})^2 ## The Attempt...

Homework Statement 1. The period of the function f(x) = tanπx + x - [x], where [.] is the greatest integer or floor function is? 2. The period of the function f(x) = sin2πx + x - [x], where [.] is the greatest integer or floor function is? Homework Equations For sin (ax+ b) + c where a,b,c...

Homework Statement A light rod of length 0.5 m has two point masses of mass 1.6 kg attached at either end. The rod is pivoted about its centre and is attached to a spring which exerts a moment on the rod that is proportional to the angle the rod is displaced from the equilibrium position and...

Homework Statement A compound pendulum consists of a thin rod of length 1.4 m and a disc of radius 0.2 m. The centre of the disc is attached to the end of the rod and the pendulum pivots about the opposite end of the rod. Both the mass of the rod and the mass of the disc are the same, each...

Homework Statement The Sun rotates on its axis every 25 days. The sun currently has a radius of 7X10^8 m. When it expands into a Red Giant (in about 4 billion years) it will have a radius of 1.5X10^11 m. What will its rotational period be assuming the same mass for both, and they are both...

Why do most mathematics literature use 2L for the period of a function? Is it related to heat equation with a rod of length L?

Why do most mathematics literature use 2L for the period of a function? Is it related to heat equation with a rod of length L?

Homework Statement Superposition of two cosine waves with different periods and different amplitudes. Homework Equations This is basically: acos(y*t) + bcos(x*t) The Attempt at a Solution I looked at different trig functions but it seems it is not a standard solution. I've found solutions...

In the far future(10^85 years) an “element” called positronium will develop with a diameter of the current observable universe of 93 billion light years. (Remember that light travels at 3 × 10^8 m/s). This element consists of an electron and a positron, both of which have a mass 9.11 × 10^−31...

Homework Statement In the Fig. What should be the initial velocity (magnitude and direction) of the arrow? Also calculate the time of flight. Homework EquationsThe Attempt at a Solution I have formulated 2 equations: v*cos(theta) * t = 20 and 3 = (v * Sin(theta) * t) + (9.81 * t^2)/2 when...

Homework Statement [/B] We are given a graph, with the information of the period, and the radius of the string. We amassed this data on our own. The graphing of it is quartic, but we have to make it into a linear graph?Homework Equations N/A The Attempt at a Solution [/B] First we tried to...

Homework Statement A block of mass M is connected to a spring of mass m and oscillates in simple harmonic motion on a horizontal, frictionless track. The force constant of the spring is k and the equilibrium length is l. Assume that all portions of the spring oscillate in phase and that the...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > Okay, I am having trouble with the units. I have the values for the wavenumber and I am trying to find the period. These are the formulas that I am trying. T = 1/f ; f = c/lambda example...

Homework Statement An electron is rotating around a proton (at rest) in a perfect circular orbit. If the radius of the orbit is r=10^-10 m, how long is the rotation period [hint: the radial acceleration is entirely due to the electric force] k=9*10^9 q=1.6*10^-19 Homework Equations 1...

Homework Statement Assume that the potential is symmetric with respect to zero and the system has amplitude ##a##, show that the period is given by : ##T=\sqrt{8m}\int^a_0\frac{dx}{\sqrt{V(a)-V(x)}}.## Homework Equations ##E = \frac12 m(\frac{dx}{dt})^2+V(x)##The Attempt at a Solution For a...

Homework Statement Attached Homework EquationsThe Attempt at a Solution I've managed to do parts i) and ii) with not much bother. But as for iii) then I haven't a clue how to show that the period of oscillation is given by that. I've always been under the impression it is simply given by...

Homework Statement A harmonic potential is parameterised as: V(x)=\frac{k}{2}(x-x_{0})^2An object moves within this potential with a total energy E > 0. (i) Where are the two turning points of the motion xA and xB? (ii) Write down the equation of motion for the object, and use it to find...

Hi, I'm using partial derivatives to calculate propagation of error. However, a bit rusty on my calculus. I'm trying to figure out the partial derivative with respect to L of the equation: 2pi*sqrt(L/g) (Yep, period of a pendulum). "g" is assumed to have no error. I know I can use the...

Greetings! I would like to know how to calculate the time, or fraction of orbital period, that a satellite spends in umbra? (total solar eclipse for satellite when they aren't affected by Solar radiation pressure and solar panels don't generate power). Information given would be satellite's...

Homework Statement To simulate the extreme accelerations during launch, astronauts train in a large centrifuge. If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of If the centrifuge diameter is 13.5m , what should be its rotation...

I did an experiment in which I varied the starting angle of elevation of a gyroscope. I noticed that at 45 degrees, the precessional period (amount of time to perform one spin) is the lowest, while at 0 degrees and 75 degrees, the precessional period is higher. If I plotted this on a graph, it...

Homework Statement [/B] A system consisting of a rod of mass M and length L is pivoted at its centre P. Two springs of spring constants k1 and k2 are attached as shown. They are relaxed when the rod is horizontal. What is the time period of the rod if it is given a slight angular displacement...

It is known that viruses arent alive. They need a host to replicate. My question is, if they need a host to replicate and stay present in the world, how can be present in the period they don't have a host to begin with? And how long can this period last, forever? It's becoming interesting for me...

Homework Statement A simple pendulum experiment is constructed from a point mass m attached to a pivot by a massless rod of length L in a constant gravitational field. The rod is released from an angle θ0 < π/2 at rest and the period of motion is found to be T0. Ignore air resistance and...

Homework Statement A mass m is sliding back and forth in a simple harmonic motion (SHM) with an amplitude A on a horizontal frictionless surface. At a point a distance L away from equilibrium, the speed of the plate is vL (vL is larger than zero). Homework Equations What is the period of the...

Homework Statement Question: If a child gets up from sitting position to standing while swinging, how does the period change? Homework Equations Period of a physical pendulum: T = 2π√(I/mgL), where I is the moment of inertia and L is the distance between the pivot and center of mass Period of...

Homework Statement The orbit of the moon is approximately a circle of radius 60 times the equatorial radius of the earth. Calculate the time taken for the Moon to complete one orbit, neglecting the rotation of the earth. Equatorial radius of the Earth = 6.4 *10^6m 1 day = 8.6*10^4s...

Homework Statement The cylindrical space station, d = 280m in diameter, rotates in order to provide artificial gravity of g for the occupants. How much time does the station take to complete one rotation? Homework Equations velocity= (2*pi*r)/period acceleration = v^2/r The Attempt at a...

Homework Statement I am actually an MD student, but I have been working on writing a novel. I wanted to create exoplanets that were suitable for human habitation, and I had a guy help me over the summer come up with plausible numbers for a variety of variables. Where I am having trouble now is...

Homework Statement I'm trying to work out the period of a function of the form sin(ax)*cos(bx), where a =/= b. I'm trying solve how the values for a and b relate to the period. I've graphed a lot of functions, but I'm struggling to notice any patterns. The period always seems somewhat related...

Homework Statement An observer is orbiting at a radius r = 3GM, \theta = \frac{\pi}{2} and \phi = \omega t where w is constant. The observer sends a photon around the circular orbit in the positive \phi direction. What is the proper time \Delta \tau for the photon to complete one orbit...

Homework Statement A large telescope of mass 8410 kg is in a circular orbit around the earth, making one revolution every 927 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth? M_E = 6.0x10^{24} kg m_s = 8410 kg T_s = 927 min = 55,620 s G =...

Suppose we have some function f(x) with period L. My book states that if it is even around the point x=L/4, it satisfies f(L/4-x)=-f(x-L/4), whilst if it is odd it satisfies f(L/4-x)=f(x-L/4). Then we define s=x-L/4 so we have for the function to be odd or even about L/4 that f(s)=±f(-s)...

Homework Statement A proton moves perpendicular to a magnetic field of .005 T. What is the period of the proton's circular orbit? Homework Equations 1. T=2pi/v 2. FB=qv x BThe Attempt at a Solution I know I need to solve for velocity first so I can use the period equation, but I don't...

A simple pendulum is suspended from a ceiling 3.2m high and the bob height from the floor is measured to be 68cm. Calculate the period of small amplitude oscillations of the bob. I converted 68cm to 0.68m. The total length of the pendulum must be 3.2 - 0.68 = 2.52. When working with the...

I want to know the way to derive the time period equation of a spring mass system accounting for the mass of the spring but not using the energy analysis method but by proceeding in the same way as we do by ignoring the mass of the spring. Please help. I did not find any texts at my level. Any...

Newton showed that if gravity at a distance R was proportional to 1/R2, then indeed the acceleration g measured at the Earth's surface would correctly predict the orbital period T of the Moon. (Remember Earths gravity causes the moon to orbit the Earth.) We can find the answer using MKS system...

1. Homework Statement Two identical moons of mass m maintain opposite positions in the same circular orbit of radius R around a planet of mass M. Find T2 the square of the orbital period. 2. Homework Equations T2=(4*pi2*R3)/ ( G*M ) [b]3. The Attempt at a Solution Hi...

Homework Statement Two satellites connected by a string revolve in concentric circular orbits of radius r and 2r Two satellites of equal masses m revolve around the planet of mass M. The satellites have extremely small mass compared to the planet, m≪M. The radii of the orbits of the...

Find the period T of the space shuttle Homework Statement (See image of problem statement for nice layout; the questions are stated below) A space shuttle of mass m is in a circular orbit of radius r around a planet of mass M in an alternate universe. In this alternate universe the laws...

Homework Statement please refer to the notes , since we know that a cycle of cosine is as in the photo 1 , why the beat period has 8 complete cycle of cosine? Homework Equations The Attempt at a Solution

Homework Statement Finding the time period of a conical pendulum by D'Alembert's principle. The string is of a constant length and all dissipations are to be ignored. Homework Equations The time period of a conical pendulum is 2\pi \sqrt{\frac{r}{g\tan\theta}}. I need to arrive at this result...

Homework Statement Prove that if f and g are periodic with period p , then f/g is also periodic, but its period could be smaller than p. The Attempt at a Solution So, the first part seems simple enough. ##\frac{f(x+p)}{g(x+p)}=\frac{f}{g}(x + p)=\frac{f}{g}(x)## But how exactly do I...

Homework Statement Determine the length of day on a planet. Imagine a planet with an acceleration at the equator of a_{equator} = 10 \,\, m/s^2 (ignoring rotation). Object dropped at equator falls with an acceleration of: a_{obj} = 9.7 \,\, m/s^2 , r = 6.2 \times 10^6 \,\, m ...

Homework Statement An iron rod of length L is hung at a common point with threads of length 'l' which are attached to the two ends of the rod. The rod is displaced a bit in the plane of the threads. What is the length of the threads if the period of the swinging of the rod is the least, and...

Homework Statement See picture : Homework Equations ##\sum M_{O}=I_{O}\ddot{\theta }## The Attempt at a Solution Consider the free-body diagram associated with an arbitrary positive angular displacement ##\theta##; The moment about point ##O## is given by ##\sum...

The problem is attached, and the official answer is given. The step in the answer does not make a lot of sense to me. How does the luminosity L converted directly into distance d, and why is the solar distance is used? And where does the dm=0.75 come from. It's just not making sense to me...

Homework Statement A spring stretches 0.150m when a 0.300kg object is hung from it. The spring is then stretched an additional 0.100m from this equilibrium point and released. A) Calculate the spring constant (k) B) Calculate the amplitude, period of motion T, frequency f and angular...

Homework Statement Suppose that you make careful observations of a pendulum on the surface of the Earth. You then move to Mars, where g is about 40% of the value on the surface of the Earth. How does the period of the pendulum on Mars compare with the period of the pendulum on Earth The period...