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,. 1/6s 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,. 1/6s after it has passed through the mean position.
Answer» Solution :Mass of the PARTICLE `m=10g=10xx10^(-3)=1xx10^(-2)kg` Time PERIOD `T=2s,omega=(2pi)/T=(2pi)/2=pi"rad"//s` Amplitude `A=5cm=5xx10^(-2)m` K.E. `=1/2mA^(2)omega^(2)COS^(2)omega t` when `t=1/6s` K.E `=1/2xx1xx10^(-2)xx(5xx10^(-2))^(2)` `(pi^(2))"cos"^(2)(pi)/6=(25xx10^(-6))/2xxpi^(2)xx((sqrt(3))/2)^(2)` `=75/8xxpi^(2)xx10^(-6)J=9.255xx10^(-5)J` `P.E =1/2mA^(2)omega^(2)SIN^(2)omegat` `=1/2xx1xx10^(-2)xx(5xx10^(-2))^(2)pi^(2)"sin"^(2)(pi)/6` `=(25xx10^(-6))/2xxpi^(2)xx(1/2)^(2)=25/8xxpi^(2)xx10^(-6)J=3.085xx10^(-5)J`