Posted by **Joey** on Wednesday, March 19, 2014 at 12:28am.

The deformation y(t) of heart muscle from its rest position after t seconds can be modelled as a spring-mass system, described by the differential equation:

my" + vy' + ky = F(t)

where m, v, and k are positive constants denoting the mass of the myocardial tissue, and the stiffness and damping coefficients, respectively; F(t) is called a forcing function.

1. In case of zero and assuming v = sqrt(4mk) ; find the general solution for the displacement of the heart tissue at time t > 0 (your answer will contain m, k, t, and arbritrary constants.)

----------------------

Alrighty so this is how I chose to attempt the question:

1. First I converted the equation to auxillary form, meaning the y" became r^2, y' became r, and y became 1. This gives me mr^2 + vr + k. I make the right-hand side = to 0 and solve using the quadratic formula. What I get is r = (sqrt(mk))/(m). This yields the solution y=e^((sqrt(mk))/(m)x).

I am having to do an alt. method for this question because it is considered an example of "repeated roots" (look at outcome of quadratic equation) so I am now having to do a full out different process from usual. Can anybody help out here? Thanks.

## Answer This Question

## Related Questions

- physics - A mass of 0.755 kg is attached to a horizontal spring of constant 403 ...
- math - A spring is stretched 5 inches abobe its rest position. Itis then ...
- physics - A mass of 0.7 kg is attached to the end of a massless spring of spring...
- Health - 3. The muscular system allows our bones to: A. Strenthen B. Contract C...
- Help with differential eqs problem???? (Calculus) - Consider the differential ...
- physics - When a 1.3kg mass was attached to a spring, the spring stretched 21cm ...
- Math - A frictionless spring with a 7-kg mass can be held stretched 1 meters ...
- math - Suppose that an object attached to a coiled spring is pulled down a ...
- calculus - Question 1: Experimentally it is found that a 6 kg weight stretches a...
- differential equations - Search: A 8 kg mass is attached to a spring hanging ...

More Related Questions