A mass 2kg is attached to the spring of spring constant 50 Nm^(-1). The block is pulled to a distance of 5 cm from its equilibrium position at x= 0 on a horizontal frictionless surface from rest at t=0. Write the expression for its displacement at anytime t.

A mass 2kg is attached to the spring of spring constant 50 Nm^(-1). Th

1.	A mass 2kg is attached to the spring of spring constant 50 Nm^(-1). The block is pulled to a distance of 5 cm from its equilibrium position at x= 0 on a horizontal frictionless surface from rest at t=0. Write the expression for its displacement at anytime t.
Answer» Solution :SPRING block system is shwon as in figure and it executes SHM with amplitude of 5 CM from mean position. Here, spring CONSTANT `k= 50 N"/"m`, amplitude A= 5cm, mass attached m = 2 kg. ANGULAR frequency `OMEGA = sqrt((k)/(m))= sqrt((50)/(2))= 5 rad"/"s`. Displacement of block at time t, `y(t) = A sin (omega t+ phi)," where "phi=` initial phase at time t=0 `y(0)= A sin (phi)` `A= A sin phi""[therefore " at time "t=0, y= +A]` `therefore 1= sin phi` `therefore phi = (pi)/(2) rad` Required equation, `y(t) = A sin(omega t+phi)` `= 5sin (omega t+(pi)/(2))` `therefore y(t) = 5 cos omega t` `y(t)= 5 cos 5t` is a required equation where t is in second and y is in cm.