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प्रश्न
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
A motion of an oscillating mercury column in a U-tube.
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उत्तर
An oscillating mercury column in a U-tube is simple harmonic. This is because the mercury moves to and fro on the same path, about the fixed position, with a certain period of time.
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 _______.
Which of the following example represent periodic motion?
An arrow released from a bow.
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
General vibrations of a polyatomic molecule about its equilibrium position.
Figure depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?
The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is its maximum speed?
Answer in brief:
Derive an expression for the period of motion of a simple pendulum. On which factors does it depend?
A person goes to bed at sharp 10.00 pm every day. Is it an example of periodic motion? If yes, what is the time period? If no, why?
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
A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and one part is used to continue the simple harmonic motion, the time period will
The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitude 2 cm, 1 m s−1 and 10 m s−2 at a certain instant. Find the amplitude and the time period of the motion.
A spring stores 5 J of energy when stretched by 25 cm. It is kept vertical with the lower end fixed. A block fastened to its other end is made to undergo small oscillations. If the block makes 5 oscillations each second what is the mass of the block?
Find the time period of the motion of the particle shown in figure . Neglect the small effect of the bend near the bottom.
Find the time period of small oscillations of the following systems. (a) A metre stick suspended through the 20 cm mark. (b) A ring of mass m and radius r suspended through a point on its periphery. (c) A uniform square plate of edge a suspended through a corner. (d) A uniform disc of mass m and radius r suspended through a point r/2 away from the centre.
A simple pendulum is inside a spacecraft. What will be its periodic time?
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.
Which of the following example represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
The motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lowermost point.
When two displacements represented by y1 = a sin(ωt) and y2 = b cos(ωt) are superimposed the motion is ______.
The equation of motion of a particle is x = a cos (αt)2. The motion is ______.
The displacement time graph of a particle executing S.H.M. is shown in figure. Which of the following statement is/are true?
- The force is zero at `t = (T)/4`.
- The acceleration is maximum at `t = (4T)/4`.
- The velocity is maximum at `t = T/4`.
- The P.E. is equal to K.E. of oscillation at `t = T/2`.
