We begin by modelling a basic mechanical example in Vensim. The system to be mod

Question

We begin by modelling a basic mechanical example in Vensim. The system to be modelled

is shown in figure 1. Assume the table is frictionless and that the string connecting the

two masses is inextensible. The spring has a stiffness constant of 10 N.m?1, m1 = 1 kg

and m2 = 0.1 kg. The initial position of m1 is 1 m to the right.

Questions

1. What is the oscillating frequency?

2. What is the maximum potential energy stored in the spring?

3. What happens when the spring constant is increased? Explain

Explanation / Answer

3) the spring constant tells you how much force you need to apply to stretch (or compress a spring) by an amount of 1 meter

so if the spring constant is 100N/m, then you have to apply a force of 100N to stretch it by one meter

the greater the value of k, the more force you need to exert to stretch/compress it

2 ) a) spring potential energy

Force in the spring

F = k x

where x is the compression in the spring. Thus, the potential energy in stored in the spring is

U = 1/2 k x^2

where this is just the integral of F. Then the potential energy stored in the spring is

U = 1/2 (150) (0.05)^2 = use your calculator

b) The max height can be calculated by realizing that all the potential energy in the spring will turn into gravitational energy, that is

U = 1/2 k x^2 = mg h

solving for h we get

h = 1/2 k x^2 / mg = 1/2 (150) (0.05)^2 / ((0.02)(9.8)) = use calculator

1 ) The lowest point is twice as far below the release point as the static equilibrium point. Thus x(static) = 0.135 m, F(static) = mg = 0.135k.

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