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let shm eqn be: x = A sin ( wt + β)
case 1: case 2:
x = A sin ( wt + β) x' = 2A sin ( wt + β)
velocity : v = Aw cos ( wt + β) v' = 2Aw cos ( wt + β)
max. speed: vmax = Aw v'max = 2Aw
for phase: v = Aw sin ( wt + β +Pi/2 ) v' = 2Aw sin ( wt + β + Pi/2 )
Acceleration : a = -Aw2 sin( wt + β) a' = -2Aw2 sin( wt + β)
energy proportional to: A2 (2A)2 = 4A2
so on doubling amplitude: frequency remains same
phase does not change
max. speed doubles
accln doubles
energy quadraples
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