Math 1 You will be required to use the method of annihilators in order to solve the differential equations .

P/S: the file is attached below. In this assignment, you will be asked to watch a short video and perform some applications that have to

do with solving second order differential equations with constant coefficients. These differential

equations can be solved using the method of annihilators. There are two primary applications that we

will be studying:

1. Spring Mass Systems

2. RLC Circuits

You can take any notes that you feel are necessary for you to understand the applications and solve for

their models. What we are primarily looking for is the function that will model the particular situation

based upon the differential equation. And then we will be discussing how we can use the D.E. and the

model to ascertain key characteristics of the modeled situation.

Spring Mass Systems:

1. Basic setup of the spring mass system. Construct a diagram of the basic spring mass system

setup and construct the differential equation. Make sure that you include what the variables in

the differential equation mean.

2. Consider the following initial-value problem for the spring mass system.

2

2

+ 2

+ = 0, (0) = −1,

(0) = 2

a. Is the system overdamped, underdamped or critically damped? Explain how you know.

b. Determine if the system passes through the equilibrium position. If it does, give the

time t.

3. Suppose that you have a spring mass system. The mass on the system is 1 g. The spring mass

constant is 25. In this situation there is no damping, but there is an external force acting on the

system that is modeled by the function, ( ) = 75 cos 5 . Construct the differential equation

for the spring mass system and then solve for ( ).

a. In this situation, is there resonance? Explain how you know.

b. Suppose that you let the spring mass continue to oscillate for a very long time, give a

function that models the movement after this very long time t (e.g. find the steady state

of the system).

RLC Circuits

1. Construct a diagram of the basic RLC Circuit and construct the differential equation. Make sure

that you include what the variables in the differential equation mean.

2. Suppose that you have a circuit with a resistance of 2 Ω, inductance of 2

11

H and a capacitance of

11

60

F. An EMF with equation of ( ) = 6 cos 4 supplies a continuous charge to the circuit.

Suppose that the q(0)= 8 V and the q’(0)=7.

3. Determine the steady state solution and transient part of the circuits current.

Spring Mass Systems:

RLC Circuits