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प्रश्न
Which of the following example represent periodic motion?
A swimmer completing one (return) trip from one bank of a river to the other and back.
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उत्तर
The swimmer’s motion is not periodic. The motion of the swimmer between the banks of a river is back and forth. However, it does not have a definite period. This is because the time taken by the swimmer during his back and forth journey may not be the same.
संबंधित प्रश्न
A seconds pendulum is suspended in an elevator moving with constant speed in downward direction. The periodic time (T) of that pendulum is _______.
Answer in brief:
Derive an expression for the period of motion of a simple pendulum. On which factors does it depend?
The length of the second’s pendulum in a clock is increased to 4 times its initial length. Calculate the number of oscillations completed by the new pendulum in one minute.
The total mechanical energy of a spring-mass system in simple harmonic motion is \[E = \frac{1}{2}m \omega^2 A^2 .\] Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same. The new mechanical energy will
A particle executes simple harmonic motion with a frequency v. The frequency with which the kinetic energy oscillates is
Two bodies A and B of equal mass are suspended from two separate massless springs of spring constant k1 and k2 respectively. If the bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of A to that of B is
A particle moves in a circular path with a uniform speed. Its motion is
A particle is fastened at the end of a string and is whirled in a vertical circle with the other end of the string being fixed. The motion of the particle is
A small block of mass m is kept on a bigger block of mass M which is attached to a vertical spring of spring constant k as shown in the figure. The system oscillates vertically. (a) Find the resultant force on the smaller block when it is displaced through a distance x above its equilibrium position. (b) Find the normal force on the smaller block at this position. When is this force smallest in magnitude? (c) What can be the maximum amplitude with which the two blocks may oscillate together?
The string the spring and the pulley shown in figure are light. Find the time period of the mass m.
The left block in figure moves at a speed v towards the right block placed in equilibrium. All collisions to take place are elastic and the surfaces are frictionless. Show that the motions of the two blocks are periodic. Find the time period of these periodic motions. Neglect the widths of the blocks.
Find the time period of the motion of the particle shown in figure . Neglect the small effect of the bend near the bottom.
A uniform disc of radius r is to be suspended through a small hole made in the disc. Find the minimum possible time period of the disc for small oscillations. What should be the distance of the hole from the centre for it to have minimum time period?
The period of oscillation of a body of mass m1 suspended from a light spring is T. When a body of mass m2 is tied to the first body and the system is made to oscillate, the period is 2T. Compare the masses m1 and m2
Find the number of oscillations performed per minute by a magnet is vibrating in the plane of a uniform field of 1.6 × 10-5 Wb/m2. The magnet has a moment of inertia 3 × 10-6 kg/m2 and magnetic moment 3 A m2.
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
The rotation of the earth about its axis.
A simple pendulum of frequency n falls freely under gravity from a certain height from the ground level. Its frequency of oscillation.
Show that the motion of a particle represented by y = sin ωt – cos ωt is simple harmonic with a period of 2π/ω.
A person normally weighing 50 kg stands on a massless platform which oscillates up and down harmonically at a frequency of 2.0 s–1 and an amplitude 5.0 cm. A weighing machine on the platform gives the persons weight against time.
- Will there be any change in weight of the body, during the oscillation?
- If answer to part (a) is yes, what will be the maximum and minimum reading in the machine and at which position?
