A circular cylinder of mass m and radius r is connected by a spring of modulus k. If it is free to roll on the rough horizontal surface without slipping, solve using Lagrange’s equation to determine its frequency.

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A: For linear systems, the superposition principle is valid whereas, for the non-linear system, the…

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Q: A makeshift compact torsional spring is made of steel (Gst = 11,000,000 psi) and is composed of a…

A: Given that a  makeshift compact torsional spring is made of steel (Gst =11,000,000 psi) and is…

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Q: A block whose mass, m is 680 g is fastened to a spring whose spring constant, k is 65 N/m. The block…

A: Mass of the block m = 680 g = 0.680 kg Spring constant k = 65 N/m Distance pulled from equilibrium…

Q: Find and find the oscillation time of an oscillator with a harmonic of amplitude 0.4m passing…

A: Amplitude is A = 0.4 m Initial velocity is v = 0.6 m/s when it passes through the origin. This is…

Q: In the following exercises assume that there's no damping.

A: Write the expression for the displacement of the mass in terms of the force and substitute the known…

Q: Find a period of small oscillations about the equilibrium position for a (5cm x 5cm x 5cm) cube of…

A: We know that density of water is 1000 kg/m3 Density of cube is 750 kg/m3. Side of cube is 5.00 cm=…

Q: A system consists of a small metallic sphere (diameter 10 cm and mass 16 kg) attached to a spring (k…

A: Given: The diameter of the metallic sphere d=10 cm. The radius of the metallic sphere r=5 cm=0.05 m.…

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Q: A block is on a horizontal surface which is moving horizontally with a simple harmonic motion of…

A: The displacement of the particle from its equilibrium position is x=xmcosωt+ϕ So, the acceleration…

Q: Consider an unknown mass m fixed to a spring with spring constant k = 22.7 N/m. It is compressed to…

A: The time period is T=total timeNo of oscillations=18.5 s11.0=1.68 s   The angular frequency is,…

Q: A mass of 1 slug is attached to a spring whose constant is 25 / 4 lb / ft. Initially the mass is…

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Q: A copper rod (length = 2.74 m, radius = 4.72 x 103 m, Young's modulus 1.1 x 1011 N/m²) hangs down…

A: The young modules of the rod is given as, Here L is the length of the rod, A is the area , Y…

Q: A door stopper spring is held at an angle from its equilibrium position and then released and the…

A: Given:- The function of angular velocity w(t)= 3e-0.2tcos(7t) Part(1)   Angular acceleration is…

Q: Problem 2: The velocities of a simple harmonic oscillator at positions X₁ and x₂ are C₁ and C₂,…

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Q: A door stopper spring is flicked from its equilibrium position, and the angular velocity of the…

A: The motion of a body around a fixed point or fixed axis is known as angular motion. It's the angle…

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Q: Consider a potential given by U(x) = -9 cos(15 x).  This potential has a stable equilibrium at x =…

A: Given: The potential is given by Ux=-9cos15x. Introduction: The time period is the time taken by a…

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

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Q: Find the angular frequency, amplitude, and phase angle of a particle of mass 2 gm that moves under a…

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Q: Find and find the oscillation time of an oscillator with a harmonic of amplitude 0.4m passing…

A: Amplitude, A = 0.4 mVelocity, v = 0.6 m/sTime period, t = ? SHM equation is given byx = A sin ωt

Q: The uniform semicircular bar of radius r = 145 mm and mass m = 3.0 kg rotates freely about a…

A: m=3.0 kgr=145 mm=0.145 m

Q: If we take the limit for the pendulum where L » r, what will the period be? Note: the symbol >>…

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Q: Q.29: A wire of length (L) and radius (r) is loaded with a weight (Mg). If (Y) and (o) denote the…

A: We have L = length of wire  r = radius of wire F = Mg = weight Y = youngs modulus

Q: An object stretches a spring 6 centimeters in equilibrium. Find its displacement for t>0 if it is…

A: This spring problem can be solved by solving differential equation.

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Q: pada дер pad 4+ 9+!!!! -+5 1901 'un|npuǝd jeo!sAud s!47 jo potuad ay7 lof uo!ssəldxǝ әу? әлџәд

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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: y. Find the ratio of the angular frequency and amplitude.

A: For a simple harmonic oscillator, the velocity can be expressed as: v=±ω√(A2-x2) where ω is the…

Q: A 100-kg mass suspended from a wire whose unstretched length is 4.00 m is found to stretch the wire…

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Q: Show neat work in Handwritten format. Don't use chatgpt,It makes no sense

A: To solve problems involving torsional moments, shear stresses, and angles of twist in materials, you…