Shock mount

%% Initialisation - SA
clc; clear; format compact; close all;

%% Variables
m=555; % System mass (kg)
k=50e3; %Equivalent k, (N/m)
g=9.81; %ms^-2
x_st=m*g/k; %Static deflection (m)

x_dot_initial=0; %Initial velocity (ms^-1)
x_initial=x_st; %Initial displacement (m)

x_dot_initial_a=1; %Initial velocity (ms^-1)
x_initial_a=0; %Initial displacement (m)
%% Calculations

w_n=sqrt(k/m); %Natural Frequency
zeta=0.05; %
c=zeta*(2*m*w_n); % Damping coefficient (Ns/m)
w_d=w_n*sqrt(1-zeta^2); %Damped Natural Frequency
B3=x_initial;
B4=(x_dot_initial+zeta*w_n*B3)/w_d;

w_n_a=sqrt(k/m); %Natural Frequency
zeta_a=0.05; %Damping factor
w_d_a=w_n_a*sqrt(1-zeta_a^2); %Damped Natural Frequency
B3_a=x_initial_a;
B4_a=(x_dot_initial_a+zeta_a*w_n_a*B3_a)/w_d_a;

%% Plot

displacement=@(t) exp(-zeta*w_n*t)*(B3.*cos(w_d*t)+B4*sin(w_d*t));
fplot(displacement, [0 10])%*2*pi/w_d]
hold on
displacement_a=@(t) exp(-zeta_a*w_n_a*t)*(B3_a.*cos(w_d_a*t)+B4_a*sin(w_d_a*t));
fplot(displacement_a, [0 10])%*2*pi/w_d]

xlabel('Time (s)'); ylabel('Displacement (m)');title('System (b): Two sets of initial conditions');
legend('Initial velocity=0 m/s, Initial displacement=x_s_t m','Initial velocity=1 m/s, Initial displacement=0 m');