m= 750; % mass of the system in kg

k= 50000; % Stiffness of system in N/m

c= 1000; % damping coefficient Ns/m

time= 0:0.01:1; %time in sec

x_0=0.01; % displacement intial condition

x_dot_0=0;

syms x(t)

D1x= diff(x,1); % differentiation

D2x= diff(x,2);

x= dsolve(m*D2x+k*x==0,x(0)==x_0, D1x(0)==x_dot_0,'t');

x_fun=matlabFunction(x) % to save solved function values

x_dot_fun = matlabFunction(diff(x));

x_t=x_fun(time);

[maxima,maxima_location]= findpeaks(x_t,time);

time_period= diff(maxima_location);

## Best Answer