man..i have 5 questions on SHM with damping..and it so difficult..it seem that the book have little coverage on this.. Qn1 A system, which is critically damped, has zero displacement at time t=0 and receive an impulse which gives it an intially velocity V. Obtain an expression for the maximum displacment in the subsequent motion. i will be using x=A exp (-rt/2m) + B*t* exp (-rt/2m) --------------> equation 1 I know that A is the amplitude...but what is B? at t=0, displacement = 0 substitute the values in equation 1 will get A=0. next, it said that it has an initial velocity = V at t=0. so i think i need to express x into velocity...so i need to differentiate dx/dt x(t)=A exp (-rt/2m) + B*t* exp (-rt/2m) dx/dt = (A) [-r/2m exp (-rt/2m)] + ( i don't know how to differentiate here...can help me..?) i think after i differentiate the dx/dt, that will be V= something...then i will put t= 0 and x= 0 all the values i will get will be put back to equation 1... what i am tryging to do correct?