मराठी
कर्नाटक बोर्ड पी.यू.सी.पीयूसी विज्ञान इयत्ता 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 - Physics

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

पर्याय

  • A

  • B

  • A + B

  • \[\sqrt{A^2 + B^2} .\]

MCQ

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 12: Simple Harmonics Motion - MCQ [पृष्ठ २५०]

APPEARS IN

एचसी वर्मा Concepts of Physics Vol. 1 [English] Class 11 and 12
पाठ 12 Simple Harmonics Motion
MCQ | Q 9 | पृष्ठ २५०

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

A particle in S.H.M. has a period of 2 seconds and amplitude of 10 cm. Calculate the acceleration when it is at 4 cm from its positive extreme position.


Define phase of S.H.M.


A particle executes S.H.M. with a period of 10 seconds. Find the time in which its potential energy will be half of its total energy.


Hence obtain the expression for acceleration, velocity and displacement of a particle performing linear S.H.M.


In measuring time period of a pendulum, it is advised to measure the time between consecutive passage through the mean position in the same direction. This is said to result in better accuracy than measuring time between consecutive passage through an extreme position. Explain.


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.


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


Which of the following quantities are always zero in a simple harmonic motion?
(a) \[\vec{F} \times \vec{a} .\]

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

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

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


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


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 small block oscillates back and forth on a smooth concave surface of radius R in Figure. Find the time period of small oscillation.


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.


A simple pendulum of length l is suspended from the ceiling of a car moving with a speed v on a circular horizontal road of radius r. (a) Find the tension in the string when it is at rest with respect to the car. (b) Find the time period of small oscillation.


What is an epoch?


Consider the Earth as a homogeneous sphere of radius R and a straight hole is bored in it through its centre. Show that a particle dropped into the hole will execute a simple harmonic motion such that its time period is

T = `2π sqrt("R"/"g")`


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 body having specific charge 8 µC/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally toward the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ______ s.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×