If the displacement (x) and velocity (v) of a particle executing simple harmonic motion are related through the expression 4 v^2=25-x^2 , then time period is

Step-by-step solution

4 v^2=25-x^2 Differentiating both the side aligned 4(2 v) d v d t & =0-2 x d x d t d v d t & =A (acceleration) d x d t & =v (velocity) aligned aligned & 8 v A=-2 x & 4 A=-x & x A =- 1 4 & Displacement Acceleration = 1 4 aligned Time period aligned T & =2 displacement acceleration & =2 1 4 =2 1 2 & = sec aligned