There is a pendulum in an elevator going down with constant velocity v. Assuming the mass of the pendulums ball is m and the length of the rod is l, write down the Lagrangian, equation of motion, and the frequency of the pendulums oscillations.

Q: A double pendulum has two degrees of freedom. Produce a reasonable Lagrangian L(01, 02, 01, 02) for…

A: The required solution is following.

Q: Consider a spring of force constant k arranged to lie in a straight line and treated as a pendulum…

A: Considering x, r  and θ as the generalized coordinates. The coordinates are given as, x1=X+l+rsinθ…

Q: 1. A spring is stretched 10 cm by a force of 3 N. A mass of 2 kg is hung from the spring and is also…

A:

Q: The following given is for questions 3 and 4: A block of mass m = 2 kg is attached to a spring with…

A: Mass of the block, m=2 kgSpring constant, k=200 N/mVelocity at x=0, vo=5 m/s The displacement of a…

Q: Considering the objects m_1 and m_2 hanging from a frictionless pulley with a mass M and radius R,…

A:

Q: You have constucted a pendulum as shown here, and by laying a meter stick underneath the pendulum,…

A: distance from one of swing to the other end (d) = 30 cm Time taken to complete one round trip (T) =…

Q: The following given is for questions 3 and 4: A block of mass m = 2 kg is attached to a spring with…

A:

Q: Consider a small mass performing simple harmonic motion with angular frequency 10 rad/s. If we know…

A: w = 10 rad/secinitial position = 5 cm initial speed = 87 cm/sec using , x = A cos(wt + ∅)put t = 0…

Q: A particle of mass m is suspended from a support by a light string of length which passes through a…

A:

Q: Anisotropic Oscillator Consider a two-dimensional anisotropic oscillator is rational (that is, ws/wy…

A: For a two dimensional anistropic oscillator the time period is when a system return to its…

Q: Consider the case of a one-dimensional harmonic ocillator. Suppose x is the displacement coordinate.…

A: Note: Thank you for the information, But as in the question, it is not mentioned that what action to…

Q: A bead of mass M is threaded on the rod of length L. The rod rotates in the horizontal plane with…

A: A bead of mass M is threaded on the rod of length L. The rod rotates in the horizontal plane with…

Q: A mass of 1.23 kg is attached to an ideal spring with a spring constant of 235 N/m and set into…

A: Given value--- mass = 1.23 kg. spring constant = 235 N/m. Amplitude = 0.08 m. speed = 0.387 m/s.…

Q: (a) For this motion, find the amplitude. (b) For this motion, find the period. (c) For this…

A:

Q: Consider a mechanical oscillator with the following characteristics: a mass of 3 kg, a damping…

A: Damping forces arise due to friction, viscosity, air drag, etc., and act in opposition to the…

Q: 1. In section 15.6, we derived an equation of motion for a simple pendulum where we assumed the mass…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: In this problem you will use the bisection method to compute the eccentric anomaly E in equation (2)…

A: To solve for the eccentric anomaly E using the bisection method, and subsequently compute the x and…

Q: Problem 5: Consider a 1D simple harmonic oscillator (without damping). (a) Compute the time averages…

A:

Q: A 5-kg mass is attached to a spring with stiffness k= 20 N/m. The mass is displaced m to the left of…

A: A massattached to a spring constantInitially i.e. at t=0sy(0)=0.25mand

Q: Our unforced spring mass model is mx00 + βx0 + kx = 0 with m, β, k > 0. We know physically that our…

A:

Q: Find the lagrangian nd eqution of motion for double pendulum where l1and l2 are the lengths of…

A: Let us consider the point O as the origin.

Q: Suppose that a mass is initially at X = Xo with an initial velocity Vo. Show that the resulting…

A:

Q: Consider the curve described by the parametric equations x = 3 cos t, y = 2 sin t. Compute the slope…

A:

Q: Anisotropic Oscillator (Anisotropic Oscillator) is a kind Consider a rational two-dimensional…

A: Given,Considering two dimentional anistropic oscillator in x and y direction.For a two dimentional…

Q: This is about a simple pendulum experiment and we used Tracker and Phyphox. Question: Based on the…

A: The error is least in the method of Accelerometer data in phyphox.  So, this method is most…

Q: An object is attached to a coiled spring. It is pulled down a distance of 20 cm from its equilibrium…

A: Given data: Amplitude (Distance the spring stretched from the equilibrium position), A=-20 cm…

Q: A spring is stretched 40 cm by a mass of 3 kg, and the mass is attached to a viscous damper that…

A: (a) Let k be defined as the spring constant. And γ be defined as the damping constant. Let Fu be…

Q: Show that the function x(t) = A cos ω1t oscillates with a frequency ν = ω1/2π. What is the frequency…

A:

Q: A mass of 10 kgs hangs from a spring with spring constant k = 136, and is attached to a viscous…

A:

Q: Obtain the Lagrangian and equations of motion for the double pendulum.

A:

Q: A mass of 55 grams stretches a spring by 8 cm. (Note that this means the forces balance, and thus mg…

A: m = 55 gram g = 981 m/s2 x= 8cm Initial velocity v= 23 cm/s = 0.23 m/s We can see that the particle…

Q: Let there be a mass M = 0.5 kg on a spring. a) If we can hang the mass on the spring in a vertical…

A:

Q: Problem 3: The motion of critically damped and overdamped oscillator systems is hardly…

A:

Q: A pendulum has a period of 5.8 s.  If you were to transfer this pendulum to the surface of Mars…

A:

Q: R(1) = (1, 1,-2), R'(1) = (-2,0, 4) and R(1) = (3,-1,1). (a) Find the vector equation of the tangent…

A:

Q: The period of a simple pendulum is found to change by 40% when its length is increased by 0.5 m.…

A:

Q: A curve in three dimensional space is parametrized as 7(u) = cos(u)i + sin(u)j + cos(3u)k, + COS u e…

A: Given, r→u=cosui^+sinuj^+cos3uk^

Q: A meter stick of total length l is pivoted a distance d from one end on a friction-less bearing. The…

A: Given, A meter stick of total length l is pivoted a distance d from one end on a friction-less…

Q: S4. At a party, you notice a disco ball (a hollow sphere of mass 0.50 kg and radius 15 cm) attached…

A:

Q: The following given is for questions 3 and 4: A block of mass m = 2 kg is attached to a spring with…

A: