A particle of mass m is located in a unidimensional potential field, where the potentialenergy of the particle depends on the coordinate x as where U0 and b are constant. Find the time period of small oscillations that the particle performs about the equilibrium position (solve the problem by Taylors method)a)b)c)d)Correct answer is option 'B'. Can you explain this answer?

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A particle of mass m is located in a unidimensional potential field, where the potential
energy of the particle depends on the coordinate x as

where U₀ and b are constant. Find the time period of small oscillations that the particle performs about the equilibrium position (solve the problem by Taylor’s method)

Correct answer is option 'B'. Can you explain this answer?

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Two springs with negligible masses and force constants k1 = 200 N/m and k2 = 160 N/m are attached to theblock of mass m = 10 kg as shown in the Fig. Initiallythe block is at rest, at the equilibrium position in which both springs are neither stretched nor compressed. At time t = 0, sharp impulse of 50 Ns is given to the blockwith a hammer along the spring

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A particle of mass m is executing oscillations about the origin on the X-axis with amplitudeA. Itspotential energy is given as U(x) =x4where is a positive constant. The x- cordinateof the particle, when the potential energy is one-third of the kinetic energy, is

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Attempt All sub parts from each question.Damping: When an analog instrument is used to measure a physical parameter, a deflecting torque is applied to the moving system which is deflected from its initial position and should move steadily to the deflected position. But due to inertia, the moving system keeps on oscillating about equilibrium. To remove the oscillation of the moving system a damping torque is required. The damping torque should be of such that the pointer quickly comes to its final steady position, without overshooting. If the instrument is underdamped, the moving system will oscillate about the final steady position with a decreasing amplitude and will take some time before it comes to rest. When the moving system moves rapidly but smoothly to its final steady position, the instrument is said to be critically damped or deadbeat. If the damping torque is more than what is required for critical damping, the instrument is said to be overdamped. In an overdamped instrument, the moving system moves slowly to its final steady position in a lethargic fashion.Methods of producing damping torque:(i) Air friction damping(ii) Fluid friction damping(iii) Eddy current dampingAir Friction Damping: A light piston is attached to the moving system. This piston moves in an air chamber closed at one end. When there is an oscillation, the piston moves in and out of the chamber. When the piston moves into the chamber, the air inside is compressed and an air pressure is built up which opposes the motion of the piston and thus the moving system faces a damping torque which ultimately reduces the oscillation. Fluid Friction Damping: In this type of damping oil is used in place of air. Viscosity of the oil being greater, the damping torque is also more. A disc is attached to the moving system which is completely dipped into the oil. When the moving system oscillates, the disc moves in oil and a frictional drag is produced. This frictional drag opposes the oscillation. Eddy Current Damping: The moving system is connected to an aluminium disc which rotates in a magnetic field. Rotation in magnetic field induces an emf in it and if the path is closed, a current (known as eddy current) flows. This current interacts with the magnetic field to produce an electromagnetic torque which opposes the motion. This torque is proportional to the oscillation of the moving system. This electromagnetic torque ultimately reduces the oscillation. Air friction damping provides a very simple and cheap method of damping. The disadvantages of fluid friction damping are that it can be used only for instruments which are in vertical position. Eddy current damping is the most efficient form of damping.Q. The most efficient form of damping is

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Attempt All sub parts from each question.Damping: When an analog instrument is used to measure a physical parameter, a deflecting torque is applied to the moving system which is deflected from its initial position and should move steadily to the deflected position. But due to inertia, the moving system keeps on oscillating about equilibrium. To remove the oscillation of the moving system a damping torque is required. The damping torque should be of such that the pointer quickly comes to its final steady position, without overshooting. If the instrument is underdamped, the moving system will oscillate about the final steady position with a decreasing amplitude and will take some time before it comes to rest. When the moving system moves rapidly but smoothly to its final steady position, the instrument is said to be critically damped or deadbeat. If the damping torque is more than what is required for critical damping, the instrument is said to be overdamped. In an overdamped instrument, the moving system moves slowly to its final steady position in a lethargic fashion.Methods of producing damping torque:(i) Air friction damping(ii) Fluid friction damping(iii) Eddy current dampingAir Friction Damping: A light piston is attached to the moving system. This piston moves in an air chamber closed at one end. When there is an oscillation, the piston moves in and out of the chamber. When the piston moves into the chamber, the air inside is compressed and an air pressure is built up which opposes the motion of the piston and thus the moving system faces a damping torque which ultimately reduces the oscillation. Fluid Friction Damping: In this type of damping oil is used in place of air. Viscosity of the oil being greater, the damping torque is also more. A disc is attached to the moving system which is completely dipped into the oil. When the moving system oscillates, the disc moves in oil and a frictional drag is produced. This frictional drag opposes the oscillation. Eddy Current Damping: The moving system is connected to an aluminium disc which rotates in a magnetic field. Rotation in magnetic field induces an emf in it and if the path is closed, a current (known as eddy current) flows. This current interacts with the magnetic field to produce an electromagnetic torque which opposes the motion. This torque is proportional to the oscillation of the moving system. This electromagnetic torque ultimately reduces the oscillation. Air friction damping provides a very simple and cheap method of damping. The disadvantages of fluid friction damping are that it can be used only for instruments which are in vertical position. Eddy current damping is the most efficient form of damping.Q. In Fluid Friction Damping the amount of damping torque

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A uniform semicircular cylinder of radius R and mass m is displaced through a small angle from its equilibrium position. It rolls without slipping during oscillations. The time periodof small oscillation is

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A particle of mass m is located in a unidimensional potential field, where the potentialenergy of the particle depends on the coordinate x as where U0 and b are constant. Find the time period of small oscillations that the particle performs about the equilibrium position (solve the problem by Taylor’s method)a)b)c)d)Correct answer is option 'B'. Can you explain this answer?

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A particle of mass m is located in a unidimensional potential field, where the potentialenergy of the particle depends on the coordinate x as where U0 and b are constant. Find the time period of small oscillations that the particle performs about the equilibrium position (solve the problem by Taylor’s method)a)b)c)d)Correct answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle of mass m is located in a unidimensional potential field, where the potentialenergy of the particle depends on the coordinate x as where U0 and b are constant. Find the time period of small oscillations that the particle performs about the equilibrium position (solve the problem by Taylor’s method)a)b)c)d)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass m is located in a unidimensional potential field, where the potentialenergy of the particle depends on the coordinate x as where U0 and b are constant. Find the time period of small oscillations that the particle performs about the equilibrium position (solve the problem by Taylor’s method)a)b)c)d)Correct answer is option 'B'. Can you explain this answer?.

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