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Define angular S.H.M. and obtain its differential equation.
Concept: Angular S.H.M. and It's Differential Equation
Using the differential equation of linear S.H.M., obtain an expression for acceleration, velocity, and displacement of simple harmonic motion.
Concept: Acceleration (a), Velocity (v) and Displacement (x) of S.H.M.
Write the differential equation for angular S.H.M.
Concept: Angular S.H.M. and It's Differential Equation
A 0.1 H inductor a 25 × 10-6 F capacitor and a 15 Ω resistor are connected in series to a 120 V, 50 Hz AC source. Calculate the resonant frequency.
Concept: Free Oscillations, Forced Oscillations and Resonance Oscillations
Derive a formula for the length of second's pendulum.
Concept: Simple Pendulum
A particle performing Linear S.H.M. has a maximum velocity 25 cm/sand maximum acceleration 100 cm/s2. Find the period of oscillations.
Concept: Differential Equation of Linear S.H.M.
Calculate the velocity of a particle performing S.H.M. after 1 second, if its displacement is given by x = `5sin((pit)/3)`m.
Concept: Acceleration (a), Velocity (v) and Displacement (x) of S.H.M.
A bar magnet of mass 120 g in the form of a rectangular parallelepiped, has dimensions l = 40 mm, b = 10 mm and h = 80 mm, with its dimension ‘h’ vertical, the magnet performs angular oscillations in the plane of the magnetic field with period π seconds. If the magnetic moment is 3.4 Am2, determine the influencing magnetic field.
Concept: Angular S.H.M. and It's Differential Equation
The displacement of a particle performing simple harmonic motion is `1/3` rd of its amplitude. What fraction of total energy will be its kinetic energy?
Concept: Linear Simple Harmonic Motion (S.H.M.)
The velocity of bob of a second’s pendulum when it is 6 cm from its mean position and amplitude of 10 cm, is ______.
Concept: Simple Pendulum
The fundamental frequency of an air column in a pipe closed at one end is in unison with the third overtone of an open pipe. Calculate the ratio of lengths of their air columns
Concept: Study of Vibrations of Air Columns
The energy of the free surface of a liquid drop is 5π times the surface tension of the liquid. Find the diameter of the drop in C.G.S. system.
Concept: Surface Tension
The surface tension of water at 0°C is 75.5 dyne/cm. Calculate surface tension of water at 25°C.
(α for water = 2.7×10-3/°C)
Concept: Surface Tension
Derive an expression for excess pressure inside a drop of liquid.
Concept: Surface Tension
What are the forced vibrations and resonance?
Concept: Free and Forced Vibrations
In a set, 21 turning forks are arranged in a series of decreasing frequencies. Each tuning fork produces 4 beats per second with the preceding fork. If the first fork is an octave of the last fork, find the frequencies of the first and tenth fork.
Concept: Study of Vibrations of Air Columns
Angle of contact for the pair of pure water with clean glass is _______.
Concept: Surface Tension
A raindrop of diameter 4 mm is about to fall on the ground. Calculate the pressure inside the raindrop. [Surface tension of water T = 0.072 N/m, atmospheric pressure = 1.013 x 105 N/m2 ]
Concept: Surface Tension
Draw a neat labelled diagram showing forces acting on the meniscus of water in a capillary tube.
Concept: Surface Tension
Wavelengths of two notes in the air are`[70/153]^m` and `[70/157]^m`. Each of these notes produces 8 beats per second with a tuning fork of fixed frequency. Find the velocity of sound in the air and frequency of the tuning fork.
Concept: Beats
