The displacement of a particle executing SHM is given by y=5 (4 t+ 3 ) . If T is the time period and the mass of the particle is 2 ~g , the kinetic energy of the particle when t= T 4 is given by

Step-by-step solution

The displacement of particle, executing SHM Velocity of particle aligned ( d y d t ) & = 5 d d t (4 t+ 3 ) & =5 (4 t+ 3 ) 4 & =20 (4 t+ 3 ) aligned Velocity at t= ( T 4 ) ( d y d t )_ t= T 4 =20 (4 T 4 + 3 ) Comparing the given equation with standard equation of SHM, given by We get aligned & y=a ( t+ ) & =4 aligned As = 2 T aligned & T= 2 & or & T= 2 4 & or & T= ( 2 ) & aligned Now, putting value of T in Eq. (ii), we get aligned u & =20 ( 2 + 3 ) & =-20 3 & =-20 3 2 & =-10 3 aligned The kinetic energy of particle,