Chapter 13 – Oscillations
A mass attached to a spring is free to oscillate, with angular velocity ω, in a horizontal plane without friction or damping. It is pulled to a distance x0 and pushed towards the centre with a velocity v0 at time t = 0. Determine the amplitude of the resulting oscillations in terms of the parameters ω,x0 and v0 . [Hint : Start with the equation x=a cos(ωt+θ) and note that the initial velocity in negative.]
13
Nov
A mass attached to a spring is free to oscillate, with angular velocity ω, in a horizontal plane without friction or damping. It is pulled to a distance x0 and pushed towards the centre with a velocity v0 at time t = 0. Determine the amplitude of the resulting oscillations in terms of the parameters [...]
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A mass attached to a spring is free to oscillate ,
In Millikan's oil drop experiment ,
The cylindrical tube of a spray pump has a cross-section of 8.0 cm^2 one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min^−1 ,
Two narrow bores of diameters 3.0mm and 6.0 mm are joined together to form a U-shaped tube open at both ends. If the U-tube contains water ,
what is the speed of ejection of the liquid through the holes ? ,
with angular velocity ω ,
A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find acceleration and velocity of the body when the displacement is
13
Nov
A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find acceleration and velocity of the body when the displacement is A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find acceleration and velocity of the body when [...]
A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillation is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring constant α is defined by the relation J=−αθ, where J is the restoring couple and θ the angle of twist).
13
Nov
A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillation is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring [...]
Tags:
In Millikan's oil drop experiment ,
The cylindrical tube of a spray pump has a cross-section of 8.0 cm^2 one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min^−1 ,
Two narrow bores of diameters 3.0mm and 6.0 mm are joined together to form a U-shaped tube open at both ends. If the U-tube contains water ,
what is the speed of ejection of the liquid through the holes ? ,
Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals the average potential energy over the same period.
13
Nov
Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals the average potential energy over the same period. Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals the average potential energy over the same period. November 13, 2020 [...]
You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags 15 cm when the entire automobile is places on it. Also the amplitude of oscillation decreases by 50% during one complete oscillation. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports 750 kg.
13
Nov
You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags 15 cm when the entire automobile is places on it. Also the amplitude of oscillation decreases by 50% during one complete oscillation. Estimate the values of (a) the spring constant [...]
Tags:
In Millikan's oil drop experiment ,
The cylindrical tube of a spray pump has a cross-section of 8.0 cm^2 one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min^−1 ,
Two narrow bores of diameters 3.0mm and 6.0 mm are joined together to form a U-shaped tube open at both ends. If the U-tube contains water ,
what is the speed of ejection of the liquid through the holes ? ,
An air chamber of volume V has a neck area of cross section A into which a ball of mass m just fits and can move up and down without any friction, figure. Show that when the ball is pressed down a little and released, it executes SHM. Obtain an expression for the time period of oscillations assuming pressure volume variations of air to be isothermal.
13
Nov
An air chamber of volume V has a neck area of cross section A into which a ball of mass m just fits and can move up and down without any friction, figure. Show that when the ball is pressed down a little and released, it executes SHM. Obtain an expression for the time period [...]
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An air chamber of volume V has a neck area of cross section A into which a ball of mass m just fits and can move up and down without any friction ,
figure. Show that when the ball is pressed down a little and released ,
it executes SHM. Obtain an expression for the time period of oscillations assuming pressure volume variations of air to be isothermal. ,
One end of a U-tube containing mercury is connected to a suction pump and the other end is connected to the atmosphere. A small pressure difference is maintained between the two columns. Show that when the suction pump is removed, the liquid in the U-tube executes SHM.
13
Nov
One end of a U-tube containing mercury is connected to a suction pump and the other end is connected to the atmosphere. A small pressure difference is maintained between the two columns. Show that when the suction pump is removed, the liquid in the U-tube executes SHM. In Millikan's oil drop experiment The cylindrical tube [...]
Tags:
In Millikan's oil drop experiment ,
The cylindrical tube of a spray pump has a cross-section of 8.0 cm^2 one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min^−1 ,
Two narrow bores of diameters 3.0mm and 6.0 mm are joined together to form a U-shaped tube open at both ends. If the U-tube contains water ,
what is the speed of ejection of the liquid through the holes ? ,
A cylindrical piece of cork of base area A and height h floats in a liquid of density ρ1. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period T = 2π hρ/ρ1g−−−−√ where ρ is the density of cork. (Ignore damping due to viscosity of the liquid).
13
Nov
A cylindrical piece of cork of base area A and height h floats in a liquid of density ρ1. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period T = 2π hρ/ρ1g−−−−√ where ρ is the density of cork. (Ignore damping due to [...]
Tags:
In Millikan's oil drop experiment ,
The cylindrical tube of a spray pump has a cross-section of 8.0 cm^2 one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min^−1 ,
Two narrow bores of diameters 3.0mm and 6.0 mm are joined together to form a U-shaped tube open at both ends. If the U-tube contains water ,
what is the speed of ejection of the liquid through the holes ? ,
A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period ?
13
Nov
A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period ? [...]
Tags:
In Millikan's oil drop experiment ,
The cylindrical tube of a spray pump has a cross-section of 8.0 cm^2 one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min^−1 ,
Two narrow bores of diameters 3.0mm and 6.0 mm are joined together to form a U-shaped tube open at both ends. If the U-tube contains water ,
what is the speed of ejection of the liquid through the holes ? ,
The acceleration due to gravity on the surface of moon is 1.7 m s^−2. What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s? (g on the surface of earth is 9.8 m s^−2 )
13
Nov
The acceleration due to gravity on the surface of moon is 1.7 m s^−2. What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s? (g on the surface of earth is 9.8 m s^−2 ) In Millikan's oil drop [...]
Tags:
In Millikan's oil drop experiment ,
The cylindrical tube of a spray pump has a cross-section of 8.0 cm^2 one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min^−1 ,
Two narrow bores of diameters 3.0mm and 6.0 mm are joined together to form a U-shaped tube open at both ends. If the U-tube contains water ,
what is the speed of ejection of the liquid through the holes ? ,