A mass attached to a spring is free to oscillate, with angular velocityω, 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 is negative.]

A mass attached to a spring is free to oscillate, with angular velocityω, 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. Read More …

A body describes simple harmonic motion with amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is (a) 5 cm, (b) 3 cm, (c) 0cm.

A body describes simple harmonic motion with amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is (a) 5 cm, (b) 3 cm, (c) 0cm.

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 oscillations 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)

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 oscillations is found to be 1.5 s. The radius of the disc Read More …

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

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 placed 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.

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 placed on it. Also, the amplitude of oscillation decreases by Read More …

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 (Fig.14.33). 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 [see Fig. 14.33].

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 (Fig.14.33). Show that when the ball is pressed down a Read More …

One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump is removed, the column of mercury in the U-tube executes simple harmonic motion.

One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump is removed, the column of mercury in Read More …

Cylindrical piece of cork of density 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/ρ1 g)  is ρ the density of cork. (Ignore damping due to viscosity of the liquid).

Cylindrical piece of cork of density 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 Read More …

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?

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 Read More …

Answer the following questions: (a) Time period of a particle in SHM depends on the force constant k and mass m of the particle: T = 2π √m/ k.A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum? (b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that T is greater than 2π √l / gThink of a qualitative argument to appreciate this result. (c) A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall? (d) What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity?

Answer the following questions: (a) Time period of a particle in SHM depends on the force constant k and mass m of the particle: T = 2π √m/ k.A simple pendulum executes SHM approximately. Why then is the time period of a pendulum Read More …

The acceleration due to gravity on the surface of moon is 1.7 ms-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 ms–2 )

The acceleration due to gravity on the surface of moon is 1.7 ms-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 Read More …

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