MAT 275 - MATLAB #5

%% Lab 5 – Jose Cabrera - MAT 275 Lab

% Solution 1

The curve in “blue” represents the equation y = y(t). Since according to the initial conditions in

LAB05ex1 the mass in the spring-mass system is displaced from its zero position. Clearly, the

curve in blue starts from at point 0.4 when t = 0. This signifies that the mass has some initial

displacement. The curve in red is at origin in the beginning which suggests that the velocity of the

mass is zero at t = 0.

% (B)

The curve y = y(t) is very similar to a sinusoidal curve. Thereby, inspecting the curve we can easily

calculate the time period.

By visual inspection the time period of the curve is approximately around 2.1s.

Analytically, we can use the equation relating the time period T and angular frequency ω

𝑇 =

2 ∗ 𝑝𝑖

𝜔

Here,

ω is equal to 3 rad/s

Hence, the time period T is equal to approx. 2.1s

% (C)

In the given system it is assumed that the damping forces are neglected. Due to this the mass will

continue to oscillate forever. Such a system is known as an ideal system as no damping forces (for

example air friction) are considered. As a result there is no force opposing the motion hence the

mass would continue to oscillate.

% (D)

From the graph it is evident that the curve in Blue is oscillating between the value +0.4 to -0.4. The

maximum displacement of the mass would be 0.4 cm.

% (E)

From the graph, the curve in Red is sinusoidal in nature and oscillates between the values +1.2 to -

1.2. Hence, the maximum velocity of the mass is also 1.2 cm/s.

All the time instants where the maximum velocity is attained by the mass -

Time (s)

0.540