The period of a particle executing shm is 2pi. The total energy of the particle is 0.0786 J. After a time pi//4sthe displacement is 0.2m. Calculate the amplitude and mass of the particle.

The period of a particle executing shm is 2pi. The total energy of the

1.	The period of a particle executing shm is 2pi. The total energy of the particle is 0.0786 J. After a time pi//4sthe displacement is 0.2m. Calculate the amplitude and mass of the particle.
Answer» Solution :Total energy = E = 0.0786 J Period `=T = 2pi` `OMEGA = (2pi)/T = (2pi)/(2pi) =1 rad//s` Displacement after a time t `= PI/4 s` is y = 0.2 m `0.2 = a sin 1 XX (pi)/4` `a= (0.2)/(sin ""pi/4)=0.2 xxsqrt2 = 0.283m` Total energy `E=1/2 momega^2a^2=1/2xxmxx1^2xx0.283^2=0.04m` `m = E/(0.04)=(0.0786)/(0.04)=1.96kg`