A simple pendulum consists of mass m suspended by a massless string of length f as shown in the figure to the right. (a) Determine the Lagrangian for this pendulum in terms of its length e and angle 0. (b) Determine Lagrange's equations of motion for this pendulum. m f ite lennth and

Q: A system having Lagrangian L=e" -mx The motion represented by the system is: (a) Free particle (b)…

A: In order to find the  nature of motion represented by the given lagrangian we need to find the…

Q: A simple pendulum of length and bob with mass m is attached to a massless support moving vertically…

A: Given: A simple pendulum having length of string,  λ Mass of bob is m and  Constant acceleration, α…

Q: Consider the pendulum illustrated below. Consider the free body diagram for the bob. The restoring…

A: The force is restoring force therefore it can be written as: In the equation, the restoring force…

Q: A mass-spring-dashpot system has mass m = 2 kg, spring constant k = 9 N/m, and drag coefficient c =…

A:

Q: Show,by integration that the moment of inertia of a uniform thin rod AB of mass 3m and length 4a…

A: Given: The mass (m) of the uniform thin rod is 3m. The length (L) of the uniform thin rod is 4a.…

Q: Let us say we have a rod with the length (L) and the mass (M) that is pivoted at its middle. This…

A:

Q: A child bounces in a harness suspended from a door frame by three elastic bands. (a) If each elastic…

A: Given: The mass of the chile is 7.15 kg. The stretching in the band is 0.21 m. The number of the…

Q: x(t) = . which means the system is (Use integers or decimals for any numbers in the expression.…

A:

Q: 21. Find the Lagrangian and Lagrange's equations for the double pendulum shown. All motion takes…

A:

Q: 3. For a critically damped system, write the solutions separately, without solving, for tstl and Dtl…

A: The condition of critical damping in which oscillator returns quickly at equilibrium point without…

Q: Two blocks and three springs below. All motion is Configured honzontal. when the blocks are als…

A: From question, 2 mass and 3 spring system.  Then kinetic energy (T) and potential energy (V) can be…

Q: Ex. 17 Show that the velocity of a particle performing S.H.M. is half the maximum V3 of its velocity…

A: To show that-(velocity of particle)=12(maximum velocity)When, x=32a

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

A:

Q: Consider a square sheet with sides: a. The sheet behaves like a compund pendulum and oscillates…

A:

Q: Find the angular frequency, amplitude, and phase angle of a particle of mass 2mg and moving by the…

A: The spring constant is F=-kxSince, F=-32x-32x=-kxk=32 N/m The relation of the angular frequency is…

Q: m The Lagrange's equation is given by 1 L ==ma²t² - mabtcos08 +mb²0² + mgbcose.

A:

Q: particle of mass m hangs from a light spring inside a lift (see figure). When the lift is at rest,…

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: Determine R such that this pendulum will have a period of one second when subjected to a small angle…

A:

Q: Prob.1 (1) State the required conditions of simple harmonic motion (SHH).

A: We need to find the necessary condition for simple harmonic motion.

Q: A mass m = 0.2 kg and a spring with constant k = 0.5 N m lie on a smooth horizontal table. The mass…

A: Horizontal mass-spring system shows simple harmonic motion (SHM) when the mass is pulled by a small…

Q: 2. A 2.5-kg block is attached to a light string of length 1.7 m. The mass moves through a fluid with…

A: Given: The mass of the block is 2.5 kg The length of the light string is 1.7 m The damping constant…

Q: State the required conditions of simple harmonic motion (SHH). Consider the torsional pendulum with…

A: (i) There are two main conditions for a motion to be classified as SHM: The magnitude of the…

Q: Find g at a point on earth where T=2.01 s for a simple pendeulum of length 1.00 m, undergoing…

A: Time period (T)=2.01 s Length(L)=1.00 m Time period==T=2πLg. Rearrange for g(acceleration due to…

Q: We have discussed in the session that the solution of the Foucault pendulum can be obtained using a…

A:

Q: Problems 3,4 For the following forcing inputs, assume u(0) = 0 and ú(0) = 0. Use Duhamel's Integral…

A: NOTE: As per Bartleby Guidelines only one part has to be solved at a time. Kindly upload other parts…

Q: 5. The amplitude of a harmonic oscillator is 5.0cm with a period of 3.0 s. The phase angle is . (a)…

A:

Q: Let’s think about the energy of the system a little bit more. Imagine there is damping (frictional)…

A:

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

A:

Q: deal with a mass-spring-dashpot sys- tem having position function x(t) satisfying Eq. (4). We write…

A: Given information: Here, x0 and v0 are the (initial condition) position and speed of the mass m at…

Q: 4. Set up the Lagrangian function for the mechanical system shown in Fig. , using the coordinates…

A:

Q: A sphere moves in simple harmonic motion with a frequency of 1.20 Hz and an amplitude of 5.20 cm.…

A:

Q: A block of mass m = 2.00 kg is attached to a spring of force constant k = 570 N/m as shown in the…

A: Given: The given mass value is, m=2.00 kg, Spring of force constant k=570 N/m, xi=5.45 cm.

Q: A particle of mass m. influence of the potential energy the Sagion xze and a>0, Determine. la the…

A: The net force acting on the particle in equilibrium condition is zero. Therefore the equilibrium…

Q: An airplane engine and the pylon that attaches it to the wing are idealized as shown below. Drive…

A: Given: An airplane engine and the pylon that attaches it to the wing. The equation of motion for all…

Q: is 5 % lower th on of the initia Problem 1 for

A: Given as,  l1=30cm, l2=70cm, n=480Hz.

Q: A cylindrical disc with a mass of 0.619 kg and radius of 0.575 m, is positioned such that it will…

A: We are given  simple harmonic motion of a physical pendulum. We have used a cylinder here. We first…

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

A: