Based on these constraints determine the mass of the object, M, to be used, and

Question

Based on these constraints determine the mass of the object, M, to be used, and also determine the value of the friction coefficient, b.

A horizontal spring mass system is to be constructed. A spring which has a spring constant of 4 will be used. The system should be designed so that it will decay like e^{-0.5 t}, and it should oscillate with a period of 3 seconds. Based on these constraints determine the mass of the object, M, to be used, and also determine the value of the friction coefficient, b.

Explanation / Answer

Initial values: v = 3m/s, s = .13m, k = 210N/m, and m = .2kg

a) at max stretch, vf = 0
Use the energy principle: Kf - Ki + Uf - Ui = 0
Since the spring is horizontal and has low friction we don't have to gravitational potential.
K = 0.5mv^2
Uspring = 0.5ks^2

0.5mvf^2 + 0.5ksf^2 = 0.5mvi^2 + 0.5ksi^2

b) at max velocity, sf = 0 use the above process

c) We know that the frequency of the spring can be found using omega = (k/m)^0.5
That value is in radians per second. To find the time interval of one cycle, use 2pi/omega. 2pi has the units radians per cycle, so this answer is in cycles per second. Lastly, we know watts is Joules per second. If we multiply the cycles per second and Joules per cycle, you get watts.

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