MAT 275 Laboratory 2

Solving Spring/Mass Systems

Consider the following differential equation form:

+ 2 + 2 = ()

Use springmass.m to generate a picture of motion for each question below (1-3). Provide the

(t) for each problem below, using the for questions 1, 2

and 3.

(1) Under-damped harmonic oscillator + 0.2 + 2 = 0, (0) = 1, (0) = 2, = 12.

Hints: = 0.1 & = 2. For < ,

() = cos (2 2 )

(2) Critically damped harmonic oscillator + 2 + = 0, (0) = 1, (0) = 2, = 12.

Hint: For = , () = +

(3) Over-damped harmonic oscillator + 4 + = 0, (0) = 1, (0) = 2, = 12.

Hint: For > ,

() = + + , = 2 2

For questions 4 , 5, and 6, use springmassdriven.m to generate a picture of motion. For each

question below provide a picture as stated above, the final solution y(t) for each problem and

provide a breakdown of the transient and with a description of motion.

(4) Driven undamped harmonic oscillator + = cos (2), (0) = 1, (0) = 0, = 24.

(5) Resonantly driven undamped harmonic oscillator + = cos (), (0) = 1, (0) = 0, = 24.

(6) Resonantly driven damped harmonic oscillator + 0.2 + 2 = cos() , (0) = 1, (0) = 0, = 24.