The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal, when displacement (amplitude = a) is
[MP PMT 1987; CPMT 1990; DPMT 1996;
MH CET 1997, 99; AFMC 1999; CPMT 2000]
Suppose at displacement y from mean position potential energy = kinetic energy
⇒12m(a2−y2)ω2=12mω2y2
⇒a2=2y2⇒y=a√2