Home
Class 11
PHYSICS
A particle is subjected to two simple ha...

A particle is subjected to two simple harmonic motions
`x_1=A_1 sinomegat`
`and x_2=A_2sin(omegat+pi/3)`
Find a the displacement at t=0, b. the maxmum speed of the particle and c. the maximum acceleration of the particle

Text Solution

Verified by Experts

a. At t=0, `x_1=A_1sinomegat=0`
`and x_2=A_2sin(omegat+pi/3)`
`=A+2sin(pi/3)=(A_2/sqrt3)/2`
Thus the resultant displacement at t=0 is
`x=x_1+x_2=(A_2sqrt3)/2`
b. The resultant of the two motions is a simple harmonic motion of the same angular frequency omega. The amplitude of the resultant motion is
`A=sqrt(A_1^2+A_2^2+2A_1A_2cos(pi/3))`
`=sqrt(A_1^2+A_2^2+A_1A_2)`
the maximum speed is
`=v_(max)=Aomega=omegasqrt(A_1^2+A_2^2+A_1A_2)`
c. The maximum acceleration is
`a_(ma)=Aomega^2=omega^2 sqrt(A_1^2+A_2^2+A_1A_2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

A particle executes two types of SHM. x_(1) = A_(1) sin omega t " and "x_(2) = A_(2) sin [omega t+(pi)/(3)] , then find the displacement at time t=0.

A particle executes two types of SHM. x_(1) = A_(1) sin omega t " and "x_(2) = A_(2) sin [omega t+(pi)/(3)] , then find the maximum speed of the particle.

A particle is subjected to two simple harmonic motions along x and y directions according to x=3sin100pit , y=4sin100pit .

A particle executes two types of SHM. x_(1) = A_(1) sin omega t " and "x_(2) = A_(2) sin [omega t+(pi)/(3)] , then find the maximum acceleration of the particle.

A particle is subjected to two mutually perpendicular simple harmonic motions such that its X and y coordinates are given by X=2 sin omegat , y=2 sin (omega+(pi)/(4)) The path of the particle will be:

A particle is acted simultaneouosly be mutually perpendicular simple harmonic motion x= a cos omega t" and "y= a sin omega t . The trajectory of motion of the particle will be………

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

A particle moves in a circle of radius 1.0cm with a speed given by v=2t , where v is in cm//s and t in seconds. (a) Find the radial acceleration of the particle at t=1s . (b) Find the tangential acceleration of the particle at t=1s . (c) Find the magnitude of net acceleration of the particle at t=1s .

A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is at the end B.

A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is at the end A.