The equation of simple harmonic motion o...

The equation of simple harmonic motion of two particle is `x_1=A_1" "sin" "omegat` and `x_2=A_2" "sin(omegat+prop)`. If they superimpose, then the amplitude of the resultant S.H.M. will be

`sqrt(A_1^2+A_2^2-2A_1A_2cosprop)`

`sqrt(A_1^2-A_2^2-2A_1A_2cosprop)`

`sqrt(A_1^2+A_2^2-2A_1A_2sinprop)`

`sqrt(A_1^2+A_2^2+2A_1A_2sinprop)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

OSCILLATIONS
TARGET PUBLICATION|Exercise COMPETITIVE THINKING|135 Videos
OSCILLATIONS
TARGET PUBLICATION|Exercise EVALUATION TEST|14 Videos
OSCILLATIONS
TARGET PUBLICATION|Exercise EVALUATION TEST|14 Videos
MODEL QUESTION PAPER
TARGET PUBLICATION|Exercise MODEL QUESTION PAPER -II|47 Videos
QUESTION PAPER 2019
TARGET PUBLICATION|Exercise MCQ|45 Videos

Similar Questions

Explore conceptually related problems

two waves y_1 = 10sin(omegat - Kx) m and y_2 = 5sin(omegat - Kx + π/3) m are superimposed. the amplitude of resultant wave is

If two simple harmonic motions are given as x_(1)=Asin omegat andx_(2)=(A//2)sinomegat+(A//2)cosomegat , then the ratio of their amplitudes is

Two parallel S.H.M.s have equations y_1=A_1sin(omegat+2pi) and y_2=A_2sin(omega/t+4pi) . The amplitude of the resultant motion is

Two simple harmonic motions are given by y_(1)=A_(1)sinomegat andy_(2)=A_(2)sin(omegat+phi) are acting on the particles in the same direction .The resultant motion is S.H.M., its amplitude is

Two progressive waves having equation x_(1) = 3 sin omegatau and x_(2) = 4 sin (omegatau + 90^(@)) are superimposed. The amplitude of the resultant wave is

(a) A particle is subjected to two simple harmonic motions x_1=A_1sin omegat and x_2=A_2 sin (omegat+pi//3) . Find (i) the displacement at t=0 , (ii) the maximum speed of the particle and (iii) the maximum acceleration of the particle. (b) A particle is subjected to two simple harmonic motions, one along the x-axis and the other on a line making an angle of 45^@ with the x-axis. The two motions are given by xy=x_0sinomegat and s=s_0sin omegat Find the amplitude of the resultant motion.

TARGET PUBLICATION-OSCILLATIONS -Critical thinking

A particle is executing SHM with amplitude A. At displacement x=(-A/4)...
Text Solution
|
Assertion: Total energy of a particle executing S.H.M. · is maximum at...
Text Solution
|
The equation of simple harmonic motion of two particle is x1=A1" "sin"...
Text Solution
|
The resultant of two S.H.M. having the same period T but different amp...
Text Solution
|
Two S.H.M.s along the same straight line in the same direction and of ...
Text Solution
|
Two S.H.M.s along the same straight line in the same direction and of ...
Text Solution
|
A simple pendulum is vibrating in an evacuated chamber, it will oscill...
Text Solution
|
If a hole is bored along the diameter of the earth and a stone is drop...
Text Solution
|
Assertion: The rotation of earth about its axis is a simple harmonic m...
Text Solution
|
A simple pendulum of length 1 m the bob performs circular motion in ho...
Text Solution
|
Restoring force acting on a pendulum, when it is deflected through an ...
Text Solution
|
The period of a simple pendulum is doubled, when
Text Solution
|
A pendulum clock thast keeps correct time on the earth is taken to the...
Text Solution
|
What is the velocity of the bob of a simple pendulum at its mean posit...
Text Solution
|
A simple pendulum of length 98cm has amplitude of 2sqrt10 cm. Taking g...
Text Solution
|
The bob of a simple pendulum of mass m and total energy E will have ma...
Text Solution
|
A carriage is sliding down an inclined plane at an angle of 60° with a...
Text Solution
|
A second's pendulum performs 100 oscillations in
Text Solution
|
A man having a wrist watch and a pendulum clock rises on a TV tower. T...
Text Solution
|
Two simple pendulum A and B of lengths 1.69m and 1.44m start swinging ...
Text Solution
|