Pendulum Definition and 1000 Threads

I am not sure which other forces I should consider besides those 3. I cannot consider tensions due to the massless rod on the masses since those will not add up to zero.

I'm interested in calculating effective gravity for a point-mass in a spinning gyro or swinging pendulum bob on a rotating planet undergoing any translational velocities and/or accelerations. I want to investigate the theoretical effects of high-energy mechanical oscillation on orbital...

I tried taking log and then diffrentiate the standard equation for time period of a pendulum but i am not getting the correct answer

The equation of motion of a simple pendulum is: $$\ddot \theta + \frac{g}{l} \theta = 0$$ Our Physics professor told us: 'If you want to become a good Physicist you have to be able to analytically check your answers to see whether they make sense'. In class he took the limits of constant...

Where: 1) ##A## is the translational acceleration, ##\Omega## the angular velocity and ##\dot \Omega## the angular acceleration (all relative to the inertial frame attached to the ground ##F##). 2) ##r'##, ##v'## and ##a'## are the position, velocity and acceleration vectors, all relative to...

I got this picture from a superconducting parametric amplifier text I was reading. (The picture is a mechanical analog of a non-degenerate parametric amplifier.) If the balls(red and blue) were oscillating at their own natural frequencies, and an external force is driven(purple), how would the...

Tried to find time in seconds in order to use the formula d=vt and find the distance in the x plane in which the target must be placed, to no avail.

Equations provided: for a spring pendulum and m replaced with L and k with g for the same pendulum, but with no weight attached. Greetings I tried solving this by stating that the length is 0,50m (since no length of the spring is given) and turning around the equation for the spring...

Hi there, First of all i want to apologize for my english, but i am not from english speaking country, so i am not perfect in it. Now for the question. I need to calculate instantaneous impact force in the lower dead center of Charpy hammer knowing nominal potential energy in lower dead center...

Summary: Question regarding graphing a T^2 x L graph for a simple pendulum I did a Simple Pendulum experiment in my college physics class the other day. We were asked to graph a T^2 x L graph based off our results. I plan on using the Length on the x-axis and the T^2 on the Y-axis. This may...

The equations is of the form of Differential algebraic Equation, of index 3.

So this question has something probably due to the conservation of angular momentum. I am able to find the moment of inertia about the pivot, which is : $$\dfrac {1}{3}mL^{2}+\left( \dfrac {1}{12}ML^{2}+mL^{2}\right) =\dfrac {17}{12}ml^{2} $$ Now to find angular velocity when angle =0, how am I...

Summary: I know that in order to keep inverted pendulum balanced when it leans forward, I should accelerate the bottom of it, but what is the force which is applied to center of mass of the pendulum with balances torque due to gravity? Is it inertial force? We assume that our inverted pendulum...

Summary: Why does segway rider who leans forward when accelerating keep balanced ? Is it because the inertial torque acting on the rider balances the torque created by gravity? F=-ma

I have been researching the rocket pendulum fallacy and have gotten into some spirited debate on the subject. If I understand correctly... 1. if the thrust is perfectly in line with the centerline (and no outside forces act on the craft other than gravity) it does not matter where the source...

I think the answer will be either (b) or (d). If the pendulum is at its amplitude when the cable breaks, then the oscillation will stop since the pendulum is also not moving at that instant. If the pendulum is at any points except amplitude, then it will hit the ceiling since it still has...

I completed this problem in two different ways, and wonder why they give different answers. Firstly, I calculate the moment of inertia of the system as I = 0.572 kg m^{2}, and the total torque acting on the system as 12.152 N. Thus I can apply the rotational analogue of NII to write...

I was solving problems about the period of a pendulum inside an elevator. They're all the same. If the elevator accelerates upwards you have that the period is shorter and it's longer if the direction is downwards. But I tried to solve something more difficult and I thought about a pendulum...

If the pendulum on the North pole is released to start it via burning the separation string, (to avoid adding an additional tangental force), wouldn't the pendulum at the time of release, already have a tangential velocity? does that effect the outcome of the experiment ? since the plane of...

Homework Statement: An adiabatic pendulum (right) is coupled via a spring with spring contant κ to a normal non-variable pendulum. The pendula have equal mass m and, initially, equal length l . The right pendulum is adiabatically pulled up with frequency ω(t) 1. Derive the equations of motion...

1) I do not quite understand how the phrase remain accurate to 1 second in 24 hours? , means ΔP = 1 second, 2) I also don't understand how pendulum period P should be 24 hours What is the reasoning for both? The solution is as such P = 2π √(L/g) P' = 2π √((L+L α δT)/g) ΔP = P'- P = 2π...

The kinetic energy of the pendulum ##K=\frac{1}{2}\cdot m\cdot v^2## will turn into heat (entirely). So both the air and the block of iron will change their temperature. To find ##n## (moles of the gas) I can use the ideal gas law: ##n=\frac{pV}{RT}=0.9 mol## Do I have the following equation...

For part a I used conservation of energy. -m*g*cos(θ)*L+1/2*m*0^2=-m*g*L +1/2*m*v^2 => v = sqrt(2*g*L(1-cos(θ )). b) For b I was think that T = mg in the equilibrium point but that doesn't invole θ in the answer. So that's why I tought that T*cos(θ ) = mg. So that the tension is mg/cos(θ). But...

is this eqn correct

Well, using the above equation it should be easy... but I can't solve it :headbang::headbang: $$ L = \frac 1 2 m (\dot l^2 + l^2 \dot \theta ^ 2) - mgl(1- \cos\theta)$$ then I guess $$\int_{t_1}^{t_2} \frac {\partial L}{\partial t} dt = L(t_2) - L(t_1)$$ *Note*: since the variation ##\frac...

Hi, I have a question regarding a pendulum and it's motion/momentum given the axis it moves around. In the below picture, there are two version of a pendulum with a weight at the bottom. It moves in and out of the screen, around an axis resting on two nails (red). My question is, how does the...

Summary: When I tried to find the angular frequency of a rod pendulum, I attempted to find its angular acceleration first, however, I realized that the results are different by using different approaches. i.e. (1) Newton's second law for a system of particles (2) Newton's second law for...

Classical problems for hookes law generally give either mass or spring constant. What if I have a graph of a wavelike structure that is oscillating which I can use to measure for example: T (period), t (time), Δx (displacement), v (velocity), a (acceleration) and other variables is this...

I imagine y - axis is parallel to direction of A and x - axis is parallel to direction of E. There are two forces acting on the pendulum: tension in direction of A and weight in direction of D. I break the weight into 2 components: W sin θ in opposite direction to tension and W cos θ in...

I'm generating poincare sections of a double pendulum, and they mostly look okay, but some of them have weird discontinuities that seem wrong. The condition for these sections is the standard ##\theta_1 = 0## and ##\dot{\theta}_1 > 0##. Looking at one of the maps, we see that most of the...

I feel like this is a dumb question, but here goes: I'm trying to model a pendulum with damping. The pendulum is connected to a rubber band (unstretched when the pendulum is vertical) on the right side, and the rubber band is fixed at the other end. How would I go about modeling a rubber band...

Hi, so I was able to solve this problem by just equating the forces (Tension, mg, and EQ). But I thought I could also solve this problem with Conservation of Energy. However, I calculated it several times, and I never get the right answer this way. Doesn't the Electric Field do the work to put...

Hi all, I'm a bit embarrassed but I'm extremely rusty with a lot of engineering principles. I've mainly been working in automation and controls within a manufacturing setting and have not done anything like this in ages. Anyways, I have a problem I need to solve and I need to determine the...

I understand how to reach $$\int_0^\phi \frac{d\theta}{\sqrt{1-k^{2}sin^{2}\theta}}=\sqrt \frac g l t$$ from physics but from there I don't get how to turn that into this new (for me) sn(u) form.

At the bottom of the circle, the tension force is greater than the weight force as there must be a net force acting towards the centre to provide the centripetal force causing the centripetal acceleration and thus the circular motion. In the equation above (T = mv^2/r + mg) I only have the mass...

First I worked out the dispersion relations, which is pretty easy: ##M \ddot x_j = K x_{j-1} + K x_{j+1} - 2K x_j -mg \frac {x_j} {l} ## (All t-derivatives) We know ##x_j## will be in the form ##Ae^{ijka}e^{-i\omega t}## so the above becomes: ## -\omega^2M = K (e^{-ika}+e^{ika}-2)-\frac {g}...

First, I decided to solve for the coefficient in front of the cosine simple harmonic function for velocity. I know there is max velocity of 30cm/s at time = 0 , so I plug it into velocity function. xmax * w = A v(t) = Acos(wt) 0.3 = Acos(w*0) A = 0.3 Then I have my velocity function...

I think my confusion on this is where the best origin for polar coordinates is. I've tried the center of the circle, and note the triangle made from the r coordinate reaching out to ##m, a,## and ##l+a\theta##. Then $$r=\sqrt{a^2+(l+a\theta)^2}$$ $$\dot r = \frac {a(l+a\theta)}...

Solving using Linear Momentum: M vb2/2 = M g 2L vb = 2√(g L) m v = m v/2 + M (2√(g L) ) v = 4 M √(g L) / m Note: I see from the answers - that this is correct. -------------- Next, I tried to solve it via Energy conservation point of view. M vb2/2 = M g 2L vb = 2√(g L) m v2/2 = m v2/8 + k...

How do I start this? I plugged the differential equation at wolfram alpha and it semmed too complicated for such an exercise. I've also looked at a sample of an answer on cheeg where the initial approach is to rewrite the equation as ##\frac{d}{dt} (\frac{\dot\theta^2}{2}-cos(\theta)) = 0## How...

Hi, So I have this question to solve and I have no idea how to do it. It states: ''How are the maximum displacements of each pendulum related for ω1 and ω2? Draw a sketch that describes the motion of the system in each case. '' The 2 angular frequencies that I have found are ω1 =√(g/l) and...

On 28 November 2018, a lecture was given by Dr. Rainer Weiss (2017 Nobel Prize Winner for Physics) at the Ontario Science Centre, Toronto. The lecture was about his work with the Laser Interferometer Gravitational-Wave Observatory (LIGO). In his lecture talked about quadruple pendulums or...

-I tried to draw the forces on the hoop when it is in the equilibrium state. I know there are friction and normal force on the contact point of the shaft and the hoop -I also put the weight force to the M object -But when i used the torque equilibrium, where the pivot is the contact point of the...

Since gravity is acting downward, I found the gravity component parallel to the plane, which was g/sin60. I substituted g/sin60 for g into that equation and got D, but the answer should be C.

Here is a picture of the problem. I have chosen the origin to lie in the middle of the circle around which the mass moves. I have also chosen the z axis to pass through the origin and through the vertex of the right circular cone. The x-axis and y-axis are so that one when curls his or her...

1. Determine the velocity of the ball when it is 30degrees from the horizontal: U1 = mgh = mg(0.8m) U2 = mgh = mg(0.4+0.4cos(30)) = mg(.74641) ΔU = U2 - U1 = mg(.74641 - .8) = mg(-0.051433) T1 =0 T2 = 0.5mv^2 ΔT = T2 - T1 = 0.5mv^2 ΔU = ΔT mg(-0.051433) = 0.5mv^2 ====> v = 1.025394 2. Use...

Homework Statement A uniform rod of mass M, and length L swings as a pendulum with two horizontal springs of negligible mass and constants k1 and k2 at the bottom end as shown in the figure. Both springs are relaxed when the when the rod is vertical. What is the period T of small oscillations...

How do I guarantee that that the friction in the movement of a simple mathematical pendulum is negligible?

Homework Statement There's the following problem (the task is to construct the Lagrangian) in the first Landau (part a): My problem is that I don't understand what did we omit exactly and why. Homework EquationsThe Attempt at a Solution I did the calculation myself (even checked with...

Homework Statement A cork ball is suspended at an angle from the vertical of a fixed cork ball below. The mass of the suspended ball is 1.5x10^-4 kg. The length of the suspension thread is .1m. The fixed ball is located .1m directly below the point of suspension of the suspended ball. Assume...