derive the time period of oscillation of a pendulum and spring and show that osillation are simple hormonic

write the energy equation spring at X extention and mass m velocity v
i.e.


<sup>differentiating both sides w.r.t dt
we get


i.e.


hence spring mass system is simple hormonic in nature

and

thus
timeperiod =

similarly proceding for pendulum one can get answer</sup>