हिंदी
कर्नाटक बोर्ड पी.यू.सी.पीयूसी विज्ञान कक्षा ११

P a Particle Moves on the X-axis According to the Equation X = a + B Sin ωT. the Motion is Simple Harmonic with Amplitude

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • A

  • B

  • A + B

  • \[\sqrt{A^2 + B^2} .\]

MCQ
Advertisements

उत्तर

B

At t = 0,

Displacement \[\left( x_0 \right)\]  is given by,   x0 = A + sin ω(0) = A

Displacement x will be maximum when sinωt is 1 or,
 xm = A + B

Amplitude will be:
xm \[-\]xo = A + B \[-\] A = B

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 12: Simple Harmonics Motion - MCQ [पृष्ठ २५०]

APPEARS IN

एचसी वर्मा Concepts of Physics Volume 1 and 2 [English]
अध्याय 12 Simple Harmonics Motion
MCQ | Q 9 | पृष्ठ २५०

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Assuming the expression for displacement of a particle starting from extreme position, explain graphically the variation of velocity and acceleration w.r.t. time.


Can simple harmonic motion take place in a non-inertial frame? If yes, should the ratio of the force applied with the displacement be constant?


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?


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.


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


A platoon of soldiers marches on a road in steps according to the sound of a marching band. The band is stopped and the soldiers are ordered to break the steps while crossing a bridge. Why?


The displacement of a particle in simple harmonic motion in one time period 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


Which of the following will change the time period as they are taken to moon?
(a) A simple pendulum
(b) A physical pendulum
(c) A torsional pendulum
(d) A spring-mass system


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.


A pendulum having time period equal to two seconds is called a seconds pendulum. Those used in pendulum clocks are of this type. Find the length of a second pendulum at a place where = π2 m/s2.


A simple pendulum of length 1 feet suspended from the ceiling of an elevator takes π/3 seconds to complete one oscillation. Find the acceleration of the elevator.


A uniform disc of mass m and radius r is suspended through a wire attached to its centre. If the time period of the torsional oscillations be T, what is the torsional constant of the wire?


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.


If the inertial mass and gravitational mass of the simple pendulum of length l are not equal, then the time period of the simple pendulum is


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.


A simple harmonic motion is given by, x = 2.4 sin ( 4πt). If distances are expressed in cm and time in seconds, the amplitude and frequency of S.H.M. are respectively, 


A spring is stretched by 5 cm by a force of 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is ______.


Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is ______.

  1. simple harmonic motion.
  2. non-periodic motion.
  3. periodic motion.
  4. periodic but not S.H.M.

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×