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The time period of a body suspended by a spring is T. What will be the new time period if the spring is cut into two equal parts and 1) the body is suspended by one part. 2) Suspended by both parts in
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A simple pendulum is executing Simple harmonic motion with a time T. If the length of the pendulum is increased by 21 %. Find the increase in its time
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A particle is executing S H M of amplitude 4 cm and T = 4 sec. find the time taken by it to move from positive extreme position to half of its
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Two linear simple harmonic motions of equal amplitudes and angular frequency w and 2 w are impressed on a particle along axis X and Y respectively. If the initial phase difference between them is `π/2` , find the resultant path followed by the
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The acceleration due to gravity on the surface of moon is 1.7 m/`s^2`. What is the time period of simple pendulum on moon if its time period on the earth is
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Using the correspondence of S. H. M. and uniform circular motion, find displacement, velocity, amplitude, time period and frequency of a particle executing
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On an average, a human heart is found to beat 75 times in a minute. Calculate its frequency and
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Which of the following functions of time represent (a) periodic and (b) non-periodic motion? Give the period for each case of periodic motion [ω is any positive constant]. sin ωt + cos
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Which of the following functions of time represent (a) periodic and (b) non-periodic motion? Give the period for each case of periodic motion [ω is any positive constant]. sin ωt + cos 2 ωt + sin 4
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Which of the following functions of time represent (a) periodic and (b) non-periodic motion? Give the period for each case of periodic motion [ω is any positive constant].
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Which of the following functions of time represent (a) periodic and (b) non-periodic motion? Give the period for each case of periodic motion [ω is any positive constant]. log
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Which of the following functions of time represent (a) simple harmonic motion and (b) periodic but not simple harmonic? Give the period for each case. (1) sin ωt – cos ωt (2) `sin^2
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The figure given below depicts two circular motions. The radius of the circle, the period of revolution, the initial position and the sense of revolution are indicated in the figures. Obtain the simple harmonic motions of the x-projection of the radius vector of the rotating particle P in each case.
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A body oscillates with SHM according to the equation (in SI units), x = 5 cos [2π t + π/4]. At t = 1.5 s, calculate the (a) displacement, (b) speed and (c) acceleration of the
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Two identical springs of spring constant k are attached to a block of mass m and to fixed supports as shown in Fig.. Show that when the mass is displaced from its equilibrium position on either side, it executes a simple harmonic motion. Find the period of oscillations.
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A block whose mass is 1 kg is fastened to a spring. The spring has a spring constant of 50 N `m^(–1)`. The block is pulled to a distance x = 10 cm from its equilibrium position at x = 0 on a frictionless surface from rest at t = 0. Calculate the kinetic, potential and total energies of the block when it is 5 cm away from the mean
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A 5 kg collar is attached to a spring of spring constant 500 N `m^(–1)`. It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by 10.0 cm and released. Calculate (a) the period of oscillation, (b) the maximum speed and (c) maximum acceleration of the
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What is the length of a simple pendulum, which ticks seconds
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For the damped oscillator shown in Fig., the mass m of the block is 200 g, k = 90 N `m^(–1)` and the damping constant b is 40 g `s^(–1)`. Calculate (a) the period of oscillation, (b) time taken for its amplitude of vibrations to drop to half of its initial value, and (c) the time taken for its mechanical energy to drop to half its initial value.
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Which of the following examples represent periodic
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