A particle performs linear S.H.M. When the displacement of the particle from mean position is 3 cm and 4 cm , corresponding velocities are 8 ~cm / s and 6 ~cm / s respectively. Its periodic time is

Step-by-step solution

We have v= A^2-x^2 Substituting the given values in the above equation we get, 8= A^2-9 ...(i) ( x =3 ~cm , v =8 cms ⁻¹ )6= A ^2-16 ...(ii) ( x =4 ~cm , v =6 cms ⁻¹ ) Diving equation (i) and (ii), array ll & 8 6 = A ^2-9 ~A ^2-16 & 4 3 = A ^2-9 ~A ^2-16 & 16 9 = A ^2-9 ~A ^2-16 & 16 ~A ^2-256=9 ~A ^2-81 & 7 ~A ^2=175 & ~A ^2= 175 7 array Substituting this value of A ^2 in equation (ii) and solving we get aligned 6 & = 175 7 -16 6 & = 175-112 7 = 9 6 & =3 & =2 & = 2 T =2 T & = seconds aligned