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Discussion Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals... 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. read less

A circular disc, of mass 10 kg, is suspended by a wire attached to its centre. The wire is twisted by... read more
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 of 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) a is defined by the relation J = – αθ, where J is the restoring couple and θ the angle of twist). read less

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration... read more
A body describes simple harmonic motion with an 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) 0 cm read less

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A mass attached to a spring is free to oscillate, with angular velocity w, in a horizontal plane without... read more
A mass attached to a spring is free to oscillate, with angular velocity w, 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 w, x0 and v0. read less

An air chamber of volume V has a neck area of cross-section into which a ball of mass m just fits and... read more
An air chamber of volume V has a neck area of cross-section into which a ball of mass m just fits and can move up and down without any friction (Fig.). Shaw 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. read less

A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so... read more
A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at 2 0°C = 340 ms-1. read less

You have learnt, that a travelling wave in one dimension is represented by a function y = f(x, t), where... read more
You have learnt, that a travelling wave in one dimension is represented by a function y = f(x, t), where x and t must appear in the combination x-vtorx + vt i.e., y =f (x ± vt). Is the converse true? That is, does every function of (x – vt) or (x + vt) represent a travelling wave? Examine, if the following functions for y can possibly represent a travelling wave? read less

A bat emits ultrasonic sound of frequency 1000 kHz in air. If this sound meets a water surface, what... read more
A bat emits ultrasonic sound of frequency 1000 kHz in air. If this sound meets a water surface, what is the wavelength of (a) the reflected sound, (b) the transmitted sound? Speed of sound in air = 340 ms-1 and in water = 1486 ms-1. read less

A hospital uses an ultrasonic scanner to locate tumours in a tissue. What is the wavelength of sound... read more
A hospital uses an ultrasonic scanner to locate tumours in a tissue. What is the wavelength of sound in a tissue in which the speed of sound is 1.7 km s-1? The operating frequency of the scanner is 4.2 MHz. read less

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A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz.... read more
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 x 10-2 kg and its linear mass density is 4.0 x 10-2 kg m-3. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string? read less

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