During SHM, A particle has displacement a from mean position If acceleration Kinetic energy and excess potential repressented by a K and U respectively then chose the appropriate graph

During SHM, A particle has displacement a from mean position If accele

1.	During SHM, A particle has displacement a from mean position If acceleration Kinetic energy and excess potential repressented by a K and U respectively then chose the appropriate graph
Answer» Solution :The KE of a particleat a DISTANCE its mean POSITION is given by `K = (1)/(2) m,(A^(2) - x^(2)) Omega^(2)` it mean curve between `K` and `x` will be parabole Hence option `(a)` and `(b)` incorrect The `PE` of a particle is given by `U = (1)/(2) m omega^(2)x^(2)` But acceleration `a = omega^(2)x`. At mean position, if wil be equal to zero and maximum at extreme position. Hence, option `(x)` is correct The sun of `PE` and `KE` is always constant it is equal is `(1)/(2) mA^(2)omega^(2)` hence `U + R = (1)/(2) m omega^(2) k^(2) M` `U = -K + (1)/(2) m omega^(2) A^(2)` If mean curve between `U` and `K` will be stranght line having position intercept on `y` axis and NEGATIVE SLOP. Hence option `(d)` is correct