Velocities of a particle executing SHM are u and v at distances `x_(1)andx_(2)` respectively from the mean position. Prove that the amplitude of the motion is
`((v^(2)x_(1)^(2)-u^(2)x_(2)^(2))/(v^(2)-u^(2)))^(1//2)`

A particle executing SHM possesses velocities v_(1)andv_(2) when it is at distances x_(1)andx_(2) respectively from its mean position. Show that, the time period of oscillation is given by T=2pi((x_(2)^(2)-x_(1)^(2))/(v_(1)^(2)-v_(2)^(2)))^(1//2) .

Velocities of a particle executing SHM are 4m*s^(-1)and3m*s^(-1) at distances 2 m and 3 m respectively from the position of equilibrium. Determine the amplitude and time period of the motion.

The maximum velocity of a particle executing SHM is v_(m)=picm*s^(-1) and the maximum acceleration is a_(m)=pi^(2)cm*s^(-2) . Determine the time period and the amplitude of motion of the particle.

Two trains, moving at velocities u_(1) and u_(2) travel along the same line towards each other. Drivers of both the trains when the trains are at a distance x apart simultaneously apply brakes producing retardations a_(1) and a_(2) , respectively. Prove that a collision can be avoided only if u_(1)^(2)a_(2)+u_(2)^(2)a_(1)=2a_(1)a_(2)x.

The equations of two SHMs are x_(1)=Asin(omegat+delta_(1))andx_(2)=Asin(omegat+delta_(2)) respectively. They superimpose on each other. Find the amplitude of the resultant.

A particle is executing SHM on x-axis starting from mean position. At time t and 2t respectively, position of the particle along x-axis are at x = M and x = N then Show time period, T=(2pit)/(cos^(-1)(N/(2M)))

If the angular frequency of a particle executing SHM is omega and its maximum velocity is v_(m) , then show that the relation between its velocity v and acceleration a is a=-omegasqrt(v_(m)^(2)-v^(2)) .

Speed of light through two media of refractive indices mu_(1) and mu_(2) are u_(1) and u_(2) respectively, then

The equation of motion of a particle executing SHM is 3(d^(2)x)/(dt^(2))=27x=0 , what will be the angular frequency of the SHM?