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if amplitude of shm is doubled wat is its effect on 1-freq 2-phase const 3-max speed 4-max acceleration 5-max energy

if amplitude of shm is doubled wat is its effect on 1-freq 2-phase const 3-max speed 4-max acceleration 5-max energy

Grade:Upto college level

1 Answers

Ramesh V
70 Points
12 years ago

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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