English
Karnataka Board PUCPUC Science Class 11

A Particle Executes Simple Harmonic Motion. If You Are Told that Its Velocity at this Instant is Zero, Can You Say What is Its Displacement? - Physics

Advertisements
Advertisements

Question

A particle executes simple harmonic motion. If you are told that its velocity at this instant is zero, can you say what is its displacement? If you are told that its velocity at this instant is maximum, can you say what is its displacement?

Short/Brief Note
Advertisements

Solution

No, we cannot say anything from the given information. To determine the displacement of the particle using its velocity at any instant, its mean position has to be known.

shaalaa.com
  Is there an error in this question or solution?
Chapter 12: Simple Harmonics Motion - Short Answers [Page 249]

APPEARS IN

HC Verma Concepts of Physics Vol. 1 [English] Class 11 and 12
Chapter 12 Simple Harmonics Motion
Short Answers | Q 4 | Page 249

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?

(a) a = 0.7x

(b) a = –200x2

(c) a = –10x

(d) a = 100x3


In a damped harmonic oscillator, periodic oscillations have _______ amplitude.

(A) gradually increasing

(B) suddenly increasing

(C) suddenly decreasing

(D) gradually decreasing


State the differential equation of linear simple harmonic motion.


A small creature moves with constant speed in a vertical circle on a bright day. Does its shadow formed by the sun on a horizontal plane move in a sample harmonic motion?


Can a pendulum clock be used in an earth-satellite?


The time period of a particle in simple harmonic motion is equal to the smallest time between the particle acquiring a particular velocity \[\vec{v}\] . The value of v is


The displacement of a particle is given by \[\overrightarrow{r} = A\left( \overrightarrow{i} \cos\omega t + \overrightarrow{j} \sin\omega t \right) .\] The motion of the particle is

 

For a particle executing simple harmonic motion, the acceleration is proportional to


A particle moves in the X-Y plane according to the equation \[\overrightarrow{r} = \left( \overrightarrow{i} + 2 \overrightarrow{j} \right)A\cos\omega t .\] 

The motion of the particle is
(a) on a straight line
(b) on an ellipse
(c) periodic
(d) simple harmonic


All the surfaces shown in figure are frictionless. The mass of the care is M, that of the block is m and the spring has spring constant k. Initially the car and the block are at rest and the spring is stretched through a length x0 when the system is released. (a) Find the amplitudes of the simple harmonic motion of the block and of the care as seen from the road. (b) Find the time period(s) of the two simple harmonic motions.


A pendulum clock giving correct time at a place where g = 9.800 m/s2 is taken to another place where it loses 24 seconds during 24 hours. Find the value of g at this new place.


A simple pendulum is constructed by hanging a heavy ball by a 5.0 m long string. It undergoes small oscillations. (a) How many oscillations does it make per second? (b) What will be the frequency if the system is taken on the moon where acceleration due to gravitation of the moon is 1.67 m/s2?


A particle is subjected to two simple harmonic motions given by x1 = 2.0 sin (100π t) and x2 = 2.0 sin (120 π t + π/3), where x is in centimeter and t in second. Find the displacement of the particle at (a) = 0.0125, (b) t = 0.025.


Write short notes on two springs connected in series.


Consider a simple pendulum of length l = 0.9 m which is properly placed on a trolley rolling down on a inclined plane which is at θ = 45° with the horizontal. Assuming that the inclined plane is frictionless, calculate the time period of oscillation of the simple pendulum.


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 varies with time according to the relation y = a sin ωt + b cos ωt.


A container consist of hemispherical shell of radius 'r ' and cylindrical shell of height 'h' radius of same material and thickness. The maximum value h/r so that container remain stable equilibrium in the position shown (neglect friction) is ______.


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?


If x = `5 sin (pi t + pi/3) m` represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×