. The equation of motion of a certain driven damped oscillator is x+7x+6x=4cos2t and initially the particle is at rest at the origin. Find the subsequent motion.

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A: Given- let the block be at a height (H = 4 m) Mass of block m=2 kg As the block is in simple…

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Q: A large block P executes horizontal simple harmonic motion as it slides across a frictionless…

A: the maximum acceleration of simple harmonic motion will be, The angular frequency is,

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A: The objective of this question is to determine the equation of motion, amplitude, period, and…

Q: The proper period of an oscillator is 1.50000 s. In an environment with damping proportional to the…

A: Given that:T=1.50000 sT'=1.50015 sE(t)=(100%-25%)Eo=0.75Eo

Q: Ex 51: A particle performing S.H.M. has a period of 6 second and amplitude 6 cm. Find the time taken…

A: We need to compute-Time required by particle (t)=?The data given as-Periodic time (T)=6 secAmplitude…

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

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Q: 4. Prove that x = Ae¯2m' cO s(@t + q) is the solution of a damped oscillation equation m d²x +b + kx…

A: Given equation of damped oscillation, md2xdt2+bdxdt+kx=0 We know, for damped oscillation,…

Q: A large block P executes horizontal simple harmonic motion as it slides across a frictionless…

A: Given,Frequency, f = 1.8 Hzμs, coefficient of static friction = 0.510

Q: For a driven damped oscillator, show that the energy dissipated per cycle by a frictional force Fa =…

A: Answer:-                 Equation of motion x = A cos ωt…

Q: Consider a driven damped oscillator with k = 32.0 N/m, m = 0.5 kg and b = 1Ns/m. The driving force…

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Q: Find the general solution?

A: Given equations are, Using (1) and (2), we get the following differential equation, This is a…

Q: A disk of radius 0.25 m is attached at its edge to a light (massless) wire of length 0.50 m to form…

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Q: A simple pendulum clock (no air resistance) has a length of 0.75 meters. The pendulum mass is…

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Q: A bathroom scale should not oscillate. Ideally it should be critically damped. Show that if it is…

A: The equation for damped oscillation be given as,

Q: child with mass of 10 kg gets into a toy car with mass of 65 kg on a playground, causing it to sink…

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Q: . Consider a particle with the an equation of motion I 26.xax = 0, where B anda are positive…

A: a)write the given differential equation as,

Q: A 16 lb weight is suspended from a spring having spring constant 5 lb/ft. Assume that an external…

A: The periodic motion is a  type of motion that repeats itself after a finite amount of time. Simple…

Q: A cube with a mass of 3.00 kg is placed on a smooth(negligible friction) horizontal surface and is…

A: To find the frequency of the resulting oscillations, we can use Hooke's Law for a mass-spring…

Q: 5.00 kg bob is connected to the ceiling via a light string, while an 8.50 kg uniform rod is also…

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Q: b) Find y(x,t) and (Express the later in terms of sinusoidal function of time, eliminating the…

A: By using normalisation formula 1st we find normalisation constant,then find wavefunction at time…

Q: A simple harmonic oscillator has a total energy of E = 12.188J. What is the potential energy when…

A: The total energy of an object under simple harmonic motion is given as E=12kA2 where A is the…

Q: A damped and driven oscillator has k = 3.0 N/m m =0.10 kg, b = 0.020 Ns/m with a driving force of…

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Q: A particle performing S.H.M. has a period of 6 second and its maximum velocity during oscillation is…

A: We need to compute the time required by particle to cover a distance of 3 cm from its mean…

Q: On a nice spring day you find yourself relaxing under an old oak tree. You pull the end of one of…

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Q: A particle of mass m, which is constrained to move along a curve in the vertical plane, performs…

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Q: A particle performs S.H.M. of amplitude 10 √2 cm. Find at what distance from the mean position the…

A: We need to compute-Displacement of particle (x) at a distance where,P.E.=K.E.Given that-Amplitude…

Q: A critically damped oscillator is represented by  ̈x + 4  ̇x + 4 x = 0, where the coefficients are…

A: The critically damped oscillator differential equation of motion is given by: x¨+4x˙+4x=0which…

Q: You exert a 183 N push the leftmost of two identical blocks of mass 262 g connected by a spring of…

A: Given Force (F)        = 183 N Mass (m)       = 262 g Stiffness (k)    = 570 kg/s2 Distance d1 = 15…

Q: A 0.1 kg object oscillates as a simple harmonic motion along the xx −axis with a frequency ff =…

A: Given : Mass of object=m=0.1 kg Frequency=f=3.185 Hz Kinetic Energy=K=0.7 J Potential Energy=P=0.3 J…

Q: A 4 ft spring measures 8 ft long after it is hung with a mass weighing 8 lb. The medium through…

A: Given data: X = displacement from equilibrium position,  m = mass attached to the spring = k =…