Boundary Value Problem based on specific problem

clear all;
close all;
clc;
%% INPUTs:
f = 6;           % Natural Cyclic Frequency (1/sec or Hertz-Hz)
x0 = 0.02;       % Initial Displacement (in m)
v0 = 0.25;       % Initial Velocity (in m/s)
%% OUTPUTs:
wn = 2*pi()*f   % Natural Circular Frequency or Angular Frequency (rad/s)

wn = 37.6991

T = 1/f         % Fundamental Time-Period (sec)

T = 0.1667

A = sqrt((x0^2) + (v0/wn)^2)    % Amplitude (m)

A = 0.0211

vm = A*wn       % Maximum Velocity (m/s)

vm = 0.7943

am = vm*wn      % Maximum Acceleration (m/s/s)

am = 29.9462

Phi = atand(x0*wn/v0) % Phase Angle (in degree)

Phi = 71.6559

syms X(t)
E = diff(X,t,2) + (wn^2)*X == 0;
x = dsolve(E)   % C1 & C2 are constant and can be determined by BCs

x = 

%% I need to find constant C1 & C2 through boundary value problem as x(0) = 0 & x'(0)=0. Can someone help me out?

Answer 1

[Torsten]

x(0) = 0 gives C1 = 0, x'(0) = 0 gives C2 = 0. Thus the solution of your equation is x = 0 for all t.

[Parvesh]

sorry my bad.

The BCs are x(0) = 0.02 & x'(0) = 0.25

[Torsten]

clear all;
close all;
clc;
%% INPUTs:
f = 6;           % Natural Cyclic Frequency (1/sec or Hertz-Hz)
x0 = 0.02;       % Initial Displacement (in m)
v0 = 0.25;       % Initial Velocity (in m/s)
%% OUTPUTs:
wn = 2*pi()*f   % Natural Circular Frequency or Angular Frequency (rad/s)

wn = 37.6991

T = 1/f         % Fundamental Time-Period (sec)

T = 0.1667

A = sqrt((x0^2) + (v0/wn)^2)    % Amplitude (m)

A = 0.0211

vm = A*wn       % Maximum Velocity (m/s)

vm = 0.7943

am = vm*wn      % Maximum Acceleration (m/s/s)

am = 29.9462

Phi = atand(x0*wn/v0) % Phase Angle (in degree)

Phi = 71.6559

syms X(t)
E = diff(X,t,2) + (wn^2)*X == 0;
dX = diff(X,t);
conds =[X(0)==0.02,dX(0)==0.25];
x = dsolve(E,conds)   % C1 & C2 are constant and can be determined by BCs

x = 

fplot(x,[0 1])