An undamped spring - mass system with mass m = 2 and a spring constant k = 8 is suddenly set in motion at time t = 0 by an external force f = 5 cos 3t . Determine the position of the mass as a function of time and draw the graph .

Expert Solution

Determine the position of the mass as a function of time and draw the graph

mu''+ku=F(t)

2u''+8u=5cos3t

u(0)=0 and u'(0)=0

u(t)=C_{1}cos2t+C_{2}sin2t-1/2cos3t

=> C_{1}=1/2 and C_{2}=0

So therefore the final solution is:

SUN BUNRA answered 2 years ago

Consider the initial value problem mx′′+cx′+kx=F(t), x(0)=0, x′(0)=0 modeling the motion of a spring-mass-dashpot system initially at rest...

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Question

An undamped spring - mass system with mass m = 2 and a spring constant k = 8 is suddenly set in motion at time t = 0 by an external force f = 5 cos 3t . Determine the position of the mass as a function of time and draw the graph .

Solutions

Expert Solution

Related Solutions

Consider the initial value problem mx′′+cx′+kx=F(t), x(0)=0, x′(0)=0 modeling the motion of a spring-mass-dashpot system initially at rest...