Period Definition and 1000 Threads

Homework Statement The orbit of an asteroid extends from the Earth’s orbit to Jupiter’s orbit, just touching both. Assume that the planetary orbits are circular and co-planar and that Newton’s constant G, the mass of the sun Ms, the mass of the asteroid ma and the radii of the Earth’s and...

Homework Statement When I was in high school I was thaught that the period of a simple harmonic oscillation (mass on spring, ball on pendulum, etc) was equal to ##T=2\pi \sqrt \frac m k## though they have never explained to me why. That's what I wanted to find out. So for example, let's take a...

Homework Statement Let γ : R → Rn be a regular (smooth) closed curve with period p. Show that there exist an orientation preserving diffeomorphism ϕ: R → R, a number p' ∈ R such that ϕ(s + p') = ϕ(s) + p and γ' = γ ◦ ϕ is an arclength parametrized closed curve with period p' Homework...

Homework Statement A pendulum obeys the equation \ddot{\theta} = -\sin(\theta) and has amplitude \theta_0 . I have to show that the period is T = 4 \int_{0}^{\frac{\pi}{2}} \frac{d\phi}{\sqrt{1-\alpha \sin^2(\phi)}} where \alpha = \sin^2(\frac{\theta_0}{2}) 2. The attempt at a solution...

What was the need for Lorentz transformation in pre-relativity period? Why was it necessary for the velocity of light to be invariant between different inertial frames and hence what was the need for Lorentz transformation when it was believed that velocity of light was constant with respect to...

Consider an algebraic variety, X which is a smooth algebraic manifold specified as the zero set of a known polynomial. I would appreciate resource recommendations preferably or an outline of approaches as to how one can compute the period matrix of X, or more precisely, of the Jacobian variety...

Homework Statement I'm currently working on the "cavendish" experiment and wish to use/develop a method separate from the casus we've been provided. Now I've nicely calculated and derived everything I need to know, including all the corrections that have to be made for the mass of the rod, the...

Homework Statement The function ##f## is defined as follows: \begin{equation*} f(t) = \begin{cases} 1, \text{ when } 2k < t < (2k+1),\\ 0, \text{ when } t = k,\\ 2, \text{ when } (2k-1) < t < 2k, & k \in \mathbb{Z}\\ \end{cases} \end{equation*} What is the period ##T## of the function ##f##...

I am given the solution to the first part of the problem, however not the second part - would appreciate for someone to double check my work! Cheers. 1. Homework Statement If a scale model of the solar system is made using materials of the same respective average density as the sun and...

Homework Statement Three identical stars, each with mass m, form the verticies of an equilateral triangle with side length d and rotate in a circular orbit due to their mutual gravitation. What is the period τ of their rotation? I set up the FBD for each star and am now trying to figure out...

Hello! First time posting here. I'm studying the IB and need to complete my required experimental write-up. I am looking to replicate the well-known experiment that finds the value of g by investigating the relationship between period and length of string for a simple pendulum. 1. Homework...

Homework Statement A landing craft with mass 1.22×10^4 kg is in a circular orbit a distance 5.50×10^5 m above the surface of a planet. The period of the orbit is 5100 s . The astronauts in the lander measure the diameter of the planet to be 9.50×10^6 m . The lander sets down at the north pole...

I have a simple complex exponential signal of the form x(t)=ejωt. To find period of the signal I tested if x(t)=x(t+nT) for all n: ejωt=ejω(t+nT) ⇒ ejωnT=1=ej2πk where n and k are integers. Then I find a general period expression as T=2πk/ωn Period T means it is the least time a signal...

Homework Statement A very light, rigid rod with a length of 0.620m extends straight out from one end of a meter stick. The stick is suspended from a pivot at the far end of the rod and is set into oscillation. (a)Determine the period of oscillation. (b)By what percentage does this differ from...

Homework Statement you are taking your pendulum clock with you to a visit of the Jupiter moon Io(radious 3643.2Km, mass 8.94X10^22 kg. calculate the duration of a full Oscillation. On the surface this oscillation time was 1s Homework Equations T=2*π√l/g[/B]The Attempt at a Solution T1/T2=√(g2/g1)

Homework Statement A satellite is in circular orbit at an altitude of 800 km above the surface of a nonrotating planet with an orbital speed of 3.7 km/s. The minimum speed needed to escape from the surface of the planet is 9.8 km/s, and G = 6.67 × 10-11 N · m2/kg2. The orbital period of the...

I am reading a text on coherent radiation and not quite understanding a particular statement. To provide some background, the authors state that coherent radiation can arise from light-matter interactions even when considering lengths, ##L##, much smaller than the wavelength (i.e. ##V \sim L^3...

Homework Statement I need to find first of all the period of Halley's comet given that: eccentricity: 0.967 perihelion: 8.8x10^7 km and AU = 1.496x10^8km Homework Equations Kepler's laws The Attempt at a Solution I think that the Perihelion = a(1-e) where a is the semi major axis. So I...

Homework Statement I need to find the period of small vertical oscillations about equilibrium position of a string whose motion can be described by the following equation: d2x/dt2 = (-g/h)*x Answer: 2π√(h/g) Homework Equations I know that the time period is given by the formula T = 2πω where...

I've got an accelerometer swinging back and forth on a string collecting data. But because of the tolerance of the accelerometer, the data is not quite clean enough to simply determine when positive turns to negative, or passes through equilibrium. Here's the data. (arbitrary reading vs. time...

Homework Statement Two smooth planes are joined at one end so that they form a V shape. The join is such that a mass placed on one of the planes will slide smoothly down one side of the V and then move up the other side. Find the period of the motion (T) of such a mass in terms of x0 (the...

Homework Statement A particle of unit mass moves in one dimension with potential V(x) = ½μ2x2 + εx4 (ε>0). Discuss the motion of the particle. If the particle released from rest at x=a (a>0) express the time period T for the particle to return to a in the form of an integral and show that when...

Homework Statement A pendulum clock is adjusted so that it keeps excellent time on the ground. The clock is brought to a mine of depth h below the ground and then raised a height h above the ground to see the differences. In which case is the error larger? Homework Equations T = 2π √(L/g) L =...

Question: A Gak it a type of alien that lives on a planet in another galaxy. One day a Gak decides to find out a little more about his planet. He drops a ball (it starts at rest) with a mass of 6.18 kg and notes that it takes 0.928 s to fall a distance of 8.37 m. The Gak’s planet orbits its sun...

I am trying to use Kepler Data for Eclipsing Binaries to estimate time period, and then other parameters such as mass, eccentricity, semi-major axis, distance, etc. of the binary systems. I want to write code in MATLAB which will use FFT to find the time period. The available data has the...

Homework Statement An object of mass ##m## moves in a smooth, straight tunnel dug between two points on the Earth’s surface. Show that the object moves with simple harmonic motion, ##a = - ω^2 x##. Find the period of this motion. You can assume that the Earth’s density is uniform. Homework...

I was asked by a friend to explain why the frequency, ##f## and period, ##T## of a wave. The initial explanation I gave to them was as follows: Heuristically, the period of a wave is defined as ##T=\frac{\text{number of units time}}{\text{cycle}}##, and its frequency as ##f=\frac{\text{number...

Hello! I need to fold some data points to a period, but I am not sure what does that mean. Some help please.

Homework Statement (a) A body of mass m is suspended from a vertical, light, helical spring of force constant k, as in Fig. 1. Write down an expression for the period T of vertical oscillations of m. (b) Two such identical springs are now joined as in Fig. 2 and support the same mass m. In...

Homework Statement a man sits in a car that makes the center gravity of the car is pulled down by 0.3 cm. After he gets out of the car, find the time period of the car while it is moving in SHM Mass of the car = 500kg Spring constant = 196,000 N/m Homework Equations ? The Attempt at a...

Homework Statement If the time period of a satellite in the orbit of radius r around a planet is T, then the time period of a satellite in the orbit of radius 4r is T'= ? 2. The attempt at a solution To be honest I have no idea how to solve this. First I thought Keplers third law may be the...

Hello, I'm trying to calculate Moon revolution period but always got 27.53 instead of 27.32. G = 6.674e-11 (m^3 kg^-1 s^-2) M = 5.9724e24 (kg) from http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html R = 384400000 (m) Earth Moon distance From 4π^2 * R^3 = GM*T^2, got moon revolution...

Recently I lend the Classical mechanics book written by Goldstein from the library, In the last page, someone scribbled this problem without any solution, I am just curious and want to give a try the problem mentioned below. I just want to know whether my approach and my solution is correct or...

Homework Statement Deduce, from the equations employed in Q4 and Q5, the exponent n in the equation: T = k rn where k is a constant and T is the period of a satellite which orbits at a radius r from a massive object in space. Hence, how long is the “year” on Venus if its distance from the Sun...

I was reading up on (discrete) Fourier transform when my mind started to think of an what-if scenario: Assumed I'm sampling a signal of the form a1*sin(b1+c1) + a2*sin(b2+c2) + a3*sin(b3+c3) + ... + aN*sin(bN+cN) + some noise where the a's represents magnitudes, b's represents frequencies and...

Homework Statement A particle with mass m is undergoing with harmonic motion with a period T, we introduce an external force F proportional to velocity v so that F= -bv with b a constant and we assume that the particle continues to oscillate how does the period change? Homework Equations F= m...

Homework Statement A rigib poll of length 2L is made into a V shape so that each leg has length L. What is the period of oscillation for small angle. The angle between the legs is 120 degrees Homework Equations 3. The Attempt at a Solution [/B] I tried to calculate the period by imagining a...

The movement of a particular piston of mass 0.85kg may be modeled with a simple harmonic. Given that its acceleration is 8m/s when 10cm from the mid position. Find the period of the motion?? I found velocity to = 1.26m/s, but I am not even sure if i need to calculate the velocity.

Homework Statement A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 2.53 hours. What is the density of the planet? Assume that the planet has a uniform density. Homework Equations T^2=(4pi^2r^3)/GM V=4/3piR^3 Density= Mass/...

what does the period of a wave , in trigonometry ... depend on ? does it depend on the ratio of the length of the sides of the right angled triangle like this ? does it depend on the angle ?? what are all the values you need to plot a graph like this ? ??

Hi everybody! I have a quick question about a pendulum. The first question of a problem asked me to find an integral expression for the time period of a pendulum without the small angle approximation, which I did and I got that: ##T(\varphi) = 4\sqrt{\frac{l}{g}} \int_{0}^{\pi/2}...

Homework Statement Homework Equations T= 2pi*sqrt(L/g) The Attempt at a Solution T= 2pi*sqrt(0.325/9.8)=1.14 s That seems like a reasonable answer. [/B]

Hello. A problem I have given my physics class states, "The distance between two crests in a wave is 1.5 m, and two crests pass a pole each second. What is the speed and period of the wave?" I believe the proper solution should be v = 3 m/s, and T = 0.5 s. In order for two crests to pass a given...

Homework Statement A stationary wave travels along a stretched string. Part of this wave at a particular instant is shown...

Homework Statement Homework Equations T=2pi√(L/g) The Attempt at a Solution I am just making sure I am doing these right. For the first one, I used the equation to determine the length it would be on Earth. The length I got was g/pi^2 = 0.993 m. I thought that it would have to stay the same...

Homework Statement The Earth's radius is 6371 km. If the Earth's radius were to increase by 30 m (0.03 km), but no change in mass, by what percentage would the Earth's rotational period increase? (Model the Earth as a uniform sphere) Homework Equations ∑Torque = Iα v = rω a = rα KE = (1/2)Iω^2...

Homework Statement We have a rod (length L, mass m) suspended at a point whose distance from the center of mass is a. 1) prove that (generally) there exist two values of a (a1, a2) for which the pendulum oscillates with the same period. 2) derive and explain: T = 2\pi\sqrt{\frac{a_1+ a_2}{g}}...

Homework Statement A doubly charged helium atom (mass = 6.68 x 10-27 kg) is accelerated through a potential difference of 4.00x 103 V. What will be the radius of curvature of the path of the atom if it is in a uniform 0.460 T magnetic field? Note: I hope this question is meant in advanced...

Homework Statement Homework Equations Find Time Period. Find the error in my solution. The Attempt at a Solution Where i am wrong ?

Consider a stable circular orbit (with a central force) subjected to small perturbations. The orbit equation is given by (3.45). The text argues that the ##\beta## in (3.46) must be a constant over the domain of ##r_0##: "Otherwise, since ##\beta## can take on only discrete rational values (for...