question_answer

The amplitude of a simple harmonic oscillator is doubled. How does this affect (i) periodic time, (ii) maximum velocity, (iii) maximum acceleration and (iv) maximum energy?                                

Answer:

                \[\text{T = 2 }\!\!\pi\!\!\text{ }\sqrt{\frac{\text{1}}{\text{Acceleration per unit displacement}}}\] As the acceleration per unit displacement is a constant quantity, T is not affected on changing the amplitude. (ii) \[{{\upsilon }_{\max }}=\omega A\] When amplitude is doubled, maximum velocity is also doubled. (iii) \[{{a}_{\max }}={{\omega }^{2}}A\] When amplitude is doubled, the maximum acceleration is also doubled. (iv) \[E=2{{\pi }^{2}}m{{v}^{2}}{{A}^{2}}\] i.e., \[E\propto {{A}^{2}}\] When amplitude is doubled, the energy of the oscillator becomes four times.