Question

1) What should the period of a spring oscillator be if it has a mass of 5 kg and a spring constant of 25 N/m? What would the new period be if the mass is doubled?

Answer 1

$Here\: in\; the\; question \; mass\; and \; spring \; constant\; is \; given:{\color{Blue} }$

                                     $T=2\pi \sqrt{M/K}$

                                    $T_{1}=2\pi \sqrt{5/25} \; \; \; \; \; ({\color{Blue} as\; the\; value\; of\; Spring\; constant\; is\; given \; K=25N/m)}$

                                     $T_{1}=2\pi \sqrt{1/5}\; second$

                                      ${\color{Red} T_{1}=2.808\; second}$     (Ans)

${\color{Blue} Now \; take\; the \; seconed\; case\; when\; mass\; is\; doubled}$ :

                    

                      :                                                    $T=2\pi \sqrt{M/K}$

                                                      $T_{2}=2\pi \sqrt{10/25}\; second$

                                                       ${\color{Red} T_{2}=3.97\; second}$       (Ans)