# submit a 1250 words paper on the topic Suspended Spring Mass System.

Hi, need to submit a 1250 words paper on the topic Suspended Spring Mass System. First, we take the Add1 block from Simulink Math Library and give two inputs M (a constant initial mass of 0.5 i.e. kg) and M* (step change mass i.e. 0.5 kg). The output of this block is MT which is the sum of both M and M*. Now this MT is further used by two blocks, 1/MT is found by taking the reciprocal of MT and Force F is found by multiplying it with gravitational constant g which is required as clearly seen from the mathematical model. Output coming from the second add block is F – (Ks) x which is multiplied by 1/MT to get the double derivative of x i.e. which is the displacement of the mass with respect to the reference position. To obtain x, it is passed through two times into the integrator block. Once we got the x, we fed into the Add block after with multiplication of Ks. The scope is attached to see the output response. This completes my model of a suspended spring-mass system for an un-damped case. As there is no damping involved in the system, so I got an oscillatory response which is shown below.

Part (1) Solution: Adding the effect of damping coefficient ‘b’ kg/s in Figure 1

Damping coefficient ‘b’ kg/s can be modeled by adding a damper in parallel with spring constant Ks.

Writing the differential equation of motion using Newton’s Law to sum to zero all of the forces acting on mass MT.

&nbsp.=Taking the Laplace transform, assuming zero initial conditions

Now we have included the damping b kg/s in the system, due to this damping system response will be under-damped, and due to this damping system will stop oscillating unlike earlier case and will reach its steady-state after some time. Simulink model for this situation and its corresponding response curves are shown.