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

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

1.	A seconds pendulum oscillates with an amplitude of 0.4 m. If the mass of the pendulum is 0.2 kg find (i) KE at the mean position, (ii) PE at the extreme position, (iii) PE at the displacement 0.2m 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 rads^(-1)` Amplitude of the pendulum A = 0.4m, MASS of the pendulum = m 0.2 kg. (i) K.E at the mean POSITION = `K.E_(" max")= (1)/(2)momega^(2)A^(2)= (1)/(2)xx 0.2 xx pi^(2) xx (0.4)^(2)= 0.1578J` (II) P.E at the EXTREME position = `P.E_(" max")= (1)/(2)m^(2)omega^(2)A^(2)= (1)/(2)xx 0.2 xx pi^(2) xx (0.4)^(2)= 0. 1578J` (iii)P.E at the displacement 0.2m `= (1)/(2)momega^(2)y^(2)= (1)/(2)xx 0.2 xx pi^(2) xx (0.2)^(2)= 0.03944J` (iv) K.E at the displacement 0.2 `m= (1)/(2)xx m^(2)omega^(2)(A^(2)-y^(2))= (1)/(2) xx 0.2 xx pi^(2) ((0.4)^(2)-(0.2)^(2))= 0.11832J`