Question

A particle performing simple harmonic motion according to y = A sinωt. Then its kinetic energy (K.E.), potential energy (P.E.) and speed (V) at position y = A/2 are

(1) \(K.E =\frac {kA^2}{8}\) , \(P.E = \frac {3kA^2}{8}\) , \(V =\frac {A}{3} \sqrt {\frac {k}{m}}\)

(2) \(K.E =\frac {3kA^2}{8}\) , \(P.E = \frac {kA^2}{8}\) , \(V =\frac {A}{2} \sqrt {\frac {3k}{m}}\)

(3) \(K.E =\frac {3kA^2}{8}\) , \(P.E = \frac {kA^2}{4}\) , \(V =A \sqrt {\frac {3k}{m}}\)

(4) \(K.E =\frac {kA^2}{4}\) , \(P.E = \frac {3kA^2}{8}\) , \(V =\frac {A}{4} \sqrt {\frac {3k}{m}}\)

Answer 1

(2) \(K.E =\frac {3kA^2}{8}\) , \(P.E = \frac {kA^2}{8}\) , \(V =\frac {A}{2} \sqrt {\frac {3k}{m}}\)