A particle of mass 10 g executes a linear SHM of amplitude 5 cm with a period of 2s. Find the P.E. and K.E.1//6 s after it has passed through the mean position.

A particle of mass 10 g executes a linear SHM of amplitude 5 cm with a

1.	A particle of mass 10 g executes a linear SHM of amplitude 5 cm with a period of 2s. Find the P.E. and K.E.1//6 s after it has passed through the mean position.
Answer» Solution :Mean of the particle`m= 10g = 10 xx 10(-3)= 1 xx 10^(-2) kg` Time PERIOD `T= 2s, OMEGA= (2pi)/(T)= (2pi)/(2)= pi "rad"//s` Amplitude `A= 5cm = 5 xx 10^(-2)m` `K.E= (1)/(2)mA^(2)omega^(2)cos^(2)omegat` when `t= (1)/(6)s` `K.E= (1)/(2) xx 1 xx 10^(-2) xx (5 xx 10^(-2))^(2)` `(pi^(2))cos^(2)((pi)/(6))= (25 xx 10^(-6))/(2)xx pi^(2) xx ((sqrt(3))/(2))^(2)= (75)/(8) xx pi^(2) xx 10^(-6) J= 9.255 xx 10^(-5)J` `P.E.= (1)/(2) mA^(2)omega^(2)SIN^(2)omegat= (1)/(2) xx 1 xx 10^(-2) xx (5 xx 10^(-2))^(2) pi^(2)sin^(2)((pi)/(6))= (25 xx 10^(-6))/(2)xx pi^(2) xx ((1)/(2))^(2)= (25)/(8) xx pi^(2) xx 10^(-6)J= 3.085 xx 10^(-5)J`