Given the Lagrangian L of the damped oscillation 1 1 ebt/mkx²
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A: Write the expression for the period of oscillation of a simple pendulum. T=2πLg
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A: The motion of a body attached to a vertical oscillating spring is given by the equation: y(t) =…
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A: It is given that, k=400 N/mx=0.10 ma=-123 m/s2V=-13.6 m/s
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A: Write the moment of inertia of the rod about the pivoted point. I=Icm+md2=mL212+mL24=mL23
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,…
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A: The damping force is proportional to the velocity of the oscillator. And given the damping constant…
Q: Show that the average velocity o particle performing S.H.M. in one oscillation 2 x (maximum…
A: To show that-Vaverage=2π(Maximum velocity)Given-(V) in S.H.M.=ωa2-x2Vmax=aωwhen x=0
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Q: For a driven damped oscillator, show that the energy dissipated per cycle by a frictional force Fa =…
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Q: The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a…
A: The period of simple pendulum is found as, T=Time takenNumber of oscillations=218 s109=2 s The…
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Q: The frequency w of the oscillator is 0.978 times the frequency w0 of the undamped oscillator. If the…
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A: let say ring is diplaced a small angle θ as shown in figure. thus torque about the point O =mgRsinθ…
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Q: Solve the following questions relating to the Harmonic Oscillator.
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Q: Show that the function x(t) = A cos ω1t oscillates with a frequency ν = ω1/2π. What is the frequency…
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Q: The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a…
A: Please see the attached image for the solution.If there are queries, please do not hesitate to ask.…
Q: Galileo (17 years old) watched a lamp suspended from the ceiling of the Cathedral in Pisa Italy, as…
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Q: The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a…
A: The objective of the question is to calculate the acceleration due to gravity (gpp) on the Pink…
Q: While seated on a tall bench, extend your lower leg a small amount and then let it swing freely…
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Q: The equation of motion of a particle in simple harmonic motion is given by: x(t) = 0.3cos(wt), where…
A: Ans. (c) 1.5 sec the equation of motion is given asxt=0.3 cosωtnow, velocity, v =dxdt=0.3-ω sin…
Q: For a simple harmonic oscillator with x=Asinωt write down an expression for the velocity.
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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…
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