Mass-Spring-Damper in Simulink and Simscape

AIM: To Analyze ‘Mass-Spring-Damper in Simulink and Simscape’

OBJECTIVES OF THE PROJECT:

1. Derive the governing equation for the model
2. Change the value of mass, damper, and spring for the Simscape model and plot the result. Change the value of Mass x0=2 in the Simulink model and plot the results
3. Make the response from Simscape and Simulink as two separate displays.

WORKFLOW:

Part :1 Derive the governing equation for the model

1. To generate the governing equation of a damped mass vibratory system in Simulink environment lets look at the summation point which has been highlighted in the figure above.
2. Looking at the output from summation block we get :

`-(k×x)-(b×v)`

Can also be re-written as :

`(k×x)-(b×dx/dt)`

Which is the R.H.S of the governing equation of a mass vibrating in a damped environment:

`(d^2 x)/dt^2 =(k/m×x)-(b/m×dx/dt)`

Hence, this is our initiating signal.

3.We can now infer that the signal after the summation block is `(d^2 x)/dt^2`

4.On multiplying it by 1/m and then integrating we can generate `b/m×dx/dt`

5.On integrating this signal we get:`x/m` and later multiply it with k(spring stiffness)

6.This is how we can model the governing equation of a spring mass damper system

Part :2

Change the value of mass, damper, and spring for the Simscape model and plot the result

Initial values assigned:

m=3.6Kg

b=10

k=400KN/m

New values:

m=5kg

b=20

k=200KN/m

We can observe that due to the high damping the Mass doesn’t vibrate for long and reaches 0m/sec velocity very every after 3 seconds into the vibration.

• Change the value of Mass & x0=2 in the Simulink model and plot the results

On changing the value of mass to 5kg and changing the x0=2 we can obtain the following plot:

We can visualize the initial position changes to 2m.

• Make the response from Simscape and Simulink as two separate displays.

We can observe that the final velocity for the Simscape model reaches around 9m/sec.

We can observe that the maximum velocity of the mass reaches around 17m/sec as we have increased the initial deformation, hence the mass vibrates accordingly.