## Find the equations of Motion

For a base excitation single DOF oscillatory system (mass-spring-damper) (like an Earthquake): Period of pi/2 sec; m = 1 kg; Spring coefficient (k) = 100 N/m; Damping Ratio = 0.15; Damper coefficient (c) = 3 N-s/m; Natural Frequency = 10 rad/s.

I want to find the equations of motion and the response given these properties and I need to use MatLab for simualtion. I’m not completely sure how to go about this with the functions, independent variable (t), and maybe ode45 to make this a consistent equation. The Equation of Motion that’s for the system is at the bottom of my script. I’m just a little lost and would appreciate some guidance. Here’s my code so far:

% For the response of a damped system under the harmonic motion of the base

k = 100 % N/m

m = 1 % kg

DR = 0.15 % Damping Ratio

wn = (k/m)^(1/2) % rad/s

w = ???

t = % independent ???

Y = % Big Y is Maximum Amplitude of Base Motion Test Bed (Unknown)

c = DR*2*m*wn %N-s/m

alpha = arctan((-c*w)/k)

A = Y*((k^2)+(c*w)^2)^(1/2)

EOM1 = A*sin(w*t-alpha) % External ForceFor a base excitation single DOF oscillatory system (mass-spring-damper) (like an Earthquake): Period of pi/2 sec; m = 1 kg; Spring coefficient (k) = 100 N/m; Damping Ratio = 0.15; Damper coefficient (c) = 3 N-s/m; Natural Frequency = 10 rad/s.

I want to find the equations of motion and the response given these properties and I need to use MatLab for simualtion. I’m not completely sure how to go about this with the functions, independent variable (t), and maybe ode45 to make this a consistent equation. The Equation of Motion that’s for the system is at the bottom of my script. I’m just a little lost and would appreciate some guidance. Here’s my code so far:

% For the response of a damped system under the harmonic motion of the base

k = 100 % N/m

m = 1 % kg

DR = 0.15 % Damping Ratio

wn = (k/m)^(1/2) % rad/s

w = ???

t = % independent ???

Y = % Big Y is Maximum Amplitude of Base Motion Test Bed (Unknown)

c = DR*2*m*wn %N-s/m

alpha = arctan((-c*w)/k)

A = Y*((k^2)+(c*w)^2)^(1/2)

EOM1 = A*sin(w*t-alpha) % External Force For a base excitation single DOF oscillatory system (mass-spring-damper) (like an Earthquake): Period of pi/2 sec; m = 1 kg; Spring coefficient (k) = 100 N/m; Damping Ratio = 0.15; Damper coefficient (c) = 3 N-s/m; Natural Frequency = 10 rad/s.

I want to find the equations of motion and the response given these properties and I need to use MatLab for simualtion. I’m not completely sure how to go about this with the functions, independent variable (t), and maybe ode45 to make this a consistent equation. The Equation of Motion that’s for the system is at the bottom of my script. I’m just a little lost and would appreciate some guidance. Here’s my code so far:

% For the response of a damped system under the harmonic motion of the base

k = 100 % N/m

m = 1 % kg

DR = 0.15 % Damping Ratio

wn = (k/m)^(1/2) % rad/s

w = ???

t = % independent ???

Y = % Big Y is Maximum Amplitude of Base Motion Test Bed (Unknown)

c = DR*2*m*wn %N-s/m

alpha = arctan((-c*w)/k)

A = Y*((k^2)+(c*w)^2)^(1/2)

EOM1 = A*sin(w*t-alpha) % External Force vibrations, differential equations, equations of motion, eom MATLAB Answers — New Questions