# Math 2250 Maple Lab 6. Mechanical Vibrations.
# L6-1
 # EXAMPLE(Wrong parameters! Change it!)             
 # Use semicolons to see what you have done.
 # Define the differential equation
 de:=3*diff(x(t),t,t)+1.5*diff(x(t),t)+4*x(t)=0:   
 # Solve the characteristic equation.
 solve(3*r^2+1.5*r+4=0,r);                         
 # Define the initial conditions
 ic:=x(0)=0,D(x)(0)= 1:                            
 # Symbolically solve for x(t)
 p:=dsolve({de,ic},x(t),method=laplace):           
 # Capture the dsolve symbolic solution as a function X(t)
 X:=unapply(rhs(p),t):                             
 # Plot the solution
 plot(X(t),t=0..5);                                

# L6-2
 #EXAMPLE(Beware! Wrong values!)
 F:=15: m:=1: k:=25: 
 c:='c': w:='w':
 C:=(w,c)->F/sqrt((k-m*w*w)^2+(c*w)^2):
 plot({C(w,4),C(w,3),C(w,2)},w=0..15,color=black);