A particle is executing simple harmonic motion. The equation of motion is given by   d2xdt2+4x=0. Then their time period of oscillation is (in seconds)

A simple harmonic motion can be represented by the equation  a=−ω2x . where  acceleration a  can be written as d2xdt2 . Hence  d2xdt2=−ω2x. Writing the given equation d2xdt2+4x=0 in the above form, we get d2xdt2=−4x . Comparing this with the above equation, we get  ω2=4. Taking square root on both sides  ω=2Using the relation  ω=2πT, we get   substitute   ω=22=2πT ⇒T=π second=time period of oscillation