A small scale model of a passenger car can be represented by the simple mass supported by a spring and a damper as shown in Fig. Q2. The vertical motion of this system can be described by the following ordinary differential equation: 𝒎𝒅𝟐𝒙𝒅𝒕𝟐+𝒄𝒅𝒙𝒅𝒕+𝒌𝒙=𝟎
where x = displacement from equilibrium position (m), t = time (s), m =mass (kg) and c = the damping coefficient (N · s/m) and k = spring constant (N/m). The mass is 20 kg. The spring constant k = 20 N/m. The initial velocity (dx/dt) is zero, and the initial displacement x = 0.5 m.
The damping coefficient c takes on three values of 5 (underdamped), 40 (critically damped), and 200 (overdamped).
A- Write and execute a computer code using ‘Octave platform’ to solve this equation over the time period 0 ≤ t ≤ 5 s for the underdamped and overdamped cases.
B- Plot the displacement (x) and velocity (dx/dt) versus time for the under damped and overdamped cases for the whole time period.
C- Compare the results using different time steps for the underdamped case only.
