A seconds pendulum oscillates with an amplitude of 0.4 m.If themass of the pendulum is 0.2 kg find (i) KE at the mean position (ii) PE at the extreme positon, (iii) PE at the displacement 0.2 m and (iv) KE at the displacement 0.2 m

A seconds pendulum oscillates with an amplitude of 0.4 m.If themass of

1.	A seconds pendulum oscillates with an amplitude of 0.4 m.If themass of the pendulum is 0.2 kg find (i) KE at the mean position (ii) PE at the extreme positon, (iii) PE at the displacement 0.2 m and (iv) KE at the displacement 0.2 m
Answer» Solution :Time period of seconds pendulum `T=2s` Angular frequency `omega=(2pi)/T=(2pi)/2=pi"rad"s^(-1)` Amplitude of the pendulum A=0.4m, masssof the pendulum =m 0.2 KG (i) K.E at the MEAN positon `=K.E_("MAX")` `=1/2m omega^(2)A^(2)=1/2xx0.2xxpi^(2)XX(0.4)^(2)=0.1578J` (II) P.E at the extreme position `=P.E_("max")` `=1/2m^(2)omega^(2)A^(2)=1/2xx0.2xxpi^(2)xx(0.4)^(2)=0.1578J` (iii) P.E at the displacement0.2 m `=1/2xxm^(2)omega^(2)y^(2)=1/2xx0.2xxpi^(2)xx(0.2)^(2)=0.03944J` (iv) K.E at the displacement 0.2 `m=1/2xxm^(2)omega^(2)(A^(2)-y^(2))` `=1/2xx0.2xxpi^(2)((0.4)^(2)-(0.2)^(2))=0.11832J`