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A Particle Executes Simple Harmonic Motion Let P Be a Point Near the Mean Position and Q Be a Point Near an Extreme. - Physics

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प्रश्न

A particle executes simple harmonic motion Let P be a point near the mean position and Q be a point near an extreme. The speed of the particle at P is larger than the speed at Q. Still the particle crosses Pand Q equal number of times in a given time interval. Does it make you unhappy?

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उत्तर

No. It does not make me unhappy because the number of times a particle crosses the mean and extreme positions does not depend on the speed of the particle.

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अध्याय 12: Simple Harmonics Motion - Short Answers [पृष्ठ २४९]

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एचसी वर्मा Concepts of Physics Vol. 1 [English] Class 11 and 12
अध्याय 12 Simple Harmonics Motion
Short Answers | Q 6 | पृष्ठ २४९

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संबंधित प्रश्न

It is proposed to move a particle in simple harmonic motion on a rough horizontal surface by applying an external force along the line of motion. Sketch the graph of the applied force against the position of the particle. Note that the applied force has two values for a given position depending on whether the particle is moving in positive or negative direction.


The energy of system in simple harmonic motion is given by \[E = \frac{1}{2}m \omega^2 A^2 .\] Which of the following two statements is more appropriate?
(A) The energy is increased because the amplitude is increased.
(B) The amplitude is increased because the energy is increased.


A hollow sphere filled with water is used as the bob of a pendulum. Assume that the equation for simple pendulum is valid with the distance between the point of suspension and centre of mass of the bob acting as the effective length of the pendulum. If water slowly leaks out of the bob, how will the time period vary?


A block of known mass is suspended from a fixed support through a light spring. Can you find the time period of vertical oscillation only by measuring the extension of the spring when the block is in equilibrium?


The force acting on a particle moving along X-axis is F = −k(x − vo t) where k is a positive constant. An observer moving at a constant velocity v0 along the X-axis looks at the particle. What kind of motion does he find for the particle?


A particle moves on the X-axis according to the equation x = A + B sin ωt. The motion is simple harmonic with amplitude


Figure represents two simple harmonic motions.

The parameter which has different values in the two motions is


The average energy in one time period in simple harmonic motion is


Select the correct statements.
(a) A simple harmonic motion is necessarily periodic.
(b) A simple harmonic motion is necessarily oscillatory.
(c) An oscillatory motion is necessarily periodic.
(d) A periodic motion is necessarily oscillatory.


Which of the following quantities are always negative in a simple harmonic motion?

(a) \[\vec{F} . \vec{a} .\]

(b) \[\vec{v} . \vec{r} .\]

(c) \[\vec{a} . \vec{r} .\]

(d)\[\vec{F} . \vec{r} .\]


A particle executes simple harmonic motion with an amplitude of 10 cm and time period 6 s. At t = 0 it is at position x = 5 cm going towards positive x-direction. Write the equation for the displacement x at time t. Find the magnitude of the acceleration of the particle at t = 4 s.


The pendulum of a certain clock has time period 2.04 s. How fast or slow does the clock run during 24 hours?


A simple pendulum fixed in a car has a time period of 4 seconds when the car is moving uniformly on a horizontal road. When the accelerator is pressed, the time period changes to 3.99 seconds. Making an approximate analysis, find the acceleration of the car.


In a simple harmonic oscillation, the acceleration against displacement for one complete oscillation will be __________.


What is an epoch?


Write short notes on two springs connected in parallel.


Consider two simple harmonic motion along the x and y-axis having the same frequencies but different amplitudes as x = A sin (ωt + φ) (along x-axis) and y = B sin ωt (along y-axis). Then show that

`"x"^2/"A"^2 + "y"^2/"B"^2 - (2"xy")/"AB" cos φ = sin^2 φ`

and also discuss the special cases when

  1. φ = 0
  2. φ = π
  3. φ = `π/2`
  4. φ = `π/2` and A = B
  5. φ = `π/4`

Note: when a particle is subjected to two simple harmonic motions at right angle to each other the particle may move along different paths. Such paths are called Lissajous figures.


The displacement of a particle is represented by the equation `y = 3 cos (pi/4 - 2ωt)`. The motion of the particle is ______.


The velocities of a particle in SHM at positions x1 and x2 are v1 and v2 respectively, its time period will be ______.


Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, and c are positive constants?


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