Math Help - Simple Harmonic Motion

1. Simple Harmonic Motion

A particle, moving in SHM has period 2T. It starts from rest. Show that it gets halfway to the centre after T/3 and attains half its maximum velocity in time T/6

2. Originally Posted by UltraGirl
A particle, moving in SHM has period 2T. It starts from rest. Show that it gets halfway to the centre after T/3 and attains half its maximum velocity in time T/6
Particle starts from rest. A = Ao at t = 0. Hence equation of SHM is
A = Aocos(ωt)
A = Ao/2
Ao/2 = Ao*cos(ωt)
1/2 = cos(ωt)
π/3 = 2π*t/2Τ
Hence t = T/3.
Velocity v = - vo*sinωt.
find t when v = vo/2.