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question_answer1) A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio m/M is
question_answer2) A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of\[{{10}^{-2}}m\]. The relative change in the angular frequency (in rad/s) of the pendulum is given by:
question_answer3) A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time (in second) it will take to drop to \[\frac{1}{1000}\] of the original amplitude is
question_answer4) Figure shows v-x graph of a particle executing simple harmonic oscillations. What is the velocity (in m/s) of the particle at \[x=3m?\]
question_answer5) Two simple pendulums of length 1m and 1.21m are started oscillating from some position. Find the minimum time (in second) after which they again start from same position.
question_answer6) A spring balance has a scale that reads 0 to 50 kg. The length of the scale is 20cm. A body suspended from this spring, when displaced and released, oscillates with a period of 0.60s. What is the weight (in Newton) of the body?
question_answer7) A pendulum is executing simple harmonic motion and its maximum kinetic energy is\[{{K}_{1}}\]. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is \[{{K}_{2}}\]. The ratio \[{{K}_{2}}/{{K}_{1}}\] is
question_answer8) The displacement of a damped harmonic oscillator is given by \[x(t)={{e}^{-0.1t}}.\cos (10\pi t+\phi )\] Here t is in seconds. The time (in second) taken for its amplitude of vibration to drop to half of its initial value is
question_answer9) Two light springs of force constants \[{{k}_{1}}\,\text{and}\,{{k}_{2}}\] and a block of mass m are in one line AB on a smooth horizontal table such that one end of each spring is fixed on rigid support and the other end is free as shown in figure. The distance CD between the free ends of springs is 60 cm. If the block moves along AB with a velocity 120 cm/s in between the springs, calculate the period (in second) of oscillation of block, \[({{k}_{1}}=1.8N/m,{{k}_{2}}=3.2N/m,\,\,m=200g)\]
question_answer10) Two particles execute simple harmonic motion of same amplitude and frequency along the same straight line. They pass one another, when going in opposite directions, each time their displacement is half of their amplitude. What is the phase difference (in degree) between them?
question_answer11) A cubical body (side 0.1m and mass 0.002 kg) float in water. It is pressed and then released, so that it oscillates vertically. Find the time period (in second).
question_answer12) Two particles execute SHM with same frequency and amplitude along the same straight line. They cross each other, at a point midway between the mean and extreme position. Find the phase difference (in degree) between them.
question_answer13) A block is kept on a horizontal table. The table is undergoing simple harmonic motion of frequency 3 Hz in a horizontal plane. The coefficient of static friction between the block and the table surface is 0.72, find the maximum amplitude (in metre) of the table in which the block does not slip on the surface. \[(g=10m/{{s}^{2}})\]:
question_answer14) A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes 5T/3. Then the ratio of m/M is
question_answer15) A pendulum has time period T in air. When it is made to oscillate in water, it acquired a time period\[T'=\sqrt{2}T\]. The specific gravity of the pendulum bob is equal to :
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