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Question # 1: Plot the position and the speed in separate graphs.

Source code:

%functionfunction dXdt=mass_spring(t,X)M=705; % (Kg)B=30; % (Nsec/m)Fa=300; % (N)K=15; % (N/m)r=1; % dX/dtdXdt(1,1)=X(2); % SpeeddXdt(2,1)=-B/M*X(2)-K/M*X(1)^r+Fa/M; %Displacement

% Program codeclear allclose allclcX0=[0;0];% (Initial speed and position)[t,X]=ode45('mass_spring',[0 200],X0);figure; plot(t,X(:,1));xlabel('Time(t)');ylabel('Speed');title('Mass spring system');legend('Speed');grid;figure;plot(t,X(:,2),'r');xlabel('Time(t)');ylabel('Position');title('Mass spring system');legend('Position');grid on;

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Question # 3:

Superpose the results and compare with the linear case r=1 and plot all three cases in the same

plot window.

Source code:

Function 1:

function dXdt=mass_spring(t,X)M=705; % (Kg)B=30; % (Nsec/m)Fa=300; % (N)K=15; % (N/m)r=1; % dX/dtdXdt(1,1)=X(2); % SpeeddXdt(2,1)=-B/M*X(2)-K/M*X(1)^r+Fa/M; % Displacement

Function 2:function dXdt=mass_spring2(t,X)M=705; % (Kg)B=30; % (Nsec/m)Fa=300; % (N)K=15; % (N/m)r=2; % dX/dtdXdt(1,1)=X(2); % SpeeddXdt(2,1)=-B/M*X(2)-K/M*X(1)^r+Fa/M; % Displacement

Function 3:

function dXdt=mass_spring3(t,X)M=705; % (Kg)B=30; % (Nsec/m)Fa=300; % (N)K=15; % (N/m)r=3; % dX/dtdXdt(1,1)=X(2); % SpeeddXdt(2,1)=-B/M*X(2)-K/M*X(1)^r+Fa/M; % Displacement

%program codingclear allclose allclcX0=[0;0];% (Initial speed and position)[t,X]=ode45('mass_spring',[0 200],X0);plot(t,X(:,1));xlabel('Time(t)');ylabel('Speed');title('Mass spring system');hold;X0=[0;0];% (Initial speed and position)[t,X]=ode45('mass_spring2',[0 200],X0);plot(t,X(:,1),'g');hold on;X0=[0;0];% (Initial speed and position)[t,X]=ode45('mass_spring3',[0 200],X0);plot(t,X(:,1),'r');legend('r = 1','r = 2','r = 3');

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grid on;figure;X0=[0;0];% (Initial speed and position)[t,X]=ode45('mass_spring',[0 200],X0);plot(t,X(:,2),'-');xlabel('Time(t)');

ylabel('Position');title('Mass spring system');hold on;X0=[0;0];% (Initial speed and position)[t,X]=ode45('mass_spring2',[0 200],X0);plot(t,X(:,2),'g');hold on;X0=[0;0];% (Initial speed and position)[t,X]=ode45('mass_spring3',[0 200],X0);plot(t,X(:,2),'r');grid on;legend('r = 1','r = 2','r = 3');title('Mass spring system');

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Question # 4:Change the values of each parameters, such as

Compare the results and describe the effects.

Answer: Source code and functions are same as question just values are changed.

Changing the value of mass M,

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When co-efficient of friction B is changed,

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When the value of elastic characteristic Kis changed,

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When Force Fa is changed,

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