A horizontal spring-mass system has low friction, spring stiffness 235 N/m, and

Question

A horizontal spring-mass system has low friction, spring stiffness 235 N/m, and mass 0.2 kg. The system is released with an initial compression of the spring of 10 cm and an initial speed of the mass of 3 m/s.

(a) What is the maximum stretch during the motion?
____ m
(b) What is the maximum speed during the motion?
____ m/s
(c) Now suppose that there is energy dissipation of 0.03 J per cycle of the spring-mass system. What is the average power input in watts required to maintain a steady oscillation?
____watt

Explanation / Answer

here,

m = 0.2 kg

spring stiffness constant , K = 235 N/m

a)

let the maximum strech be A

0.5 * k * A^2 = 0.5 * m * u^2 + 0.5 * k * xi^2

235 * A^2 = 0.2 * 3^2 + 235 * 0.1^2

A = 0.13 m

b)

let the maximum speed be v

using conservation of energy

0.5 * m*v^2 = 0.5 * m * u^2 + 0.5 * k * xi^2

0.2 * v^2 = 0.2 * 3^2 + 235 * 0.1^2

v = 4.56 m/s

c)

let the time period be T

v = A * w

4.56 = 0.13 * ( 2 * pi /T)

T = 0.179 s

the average power input in watts required to maintain a steady oscillation, P = E/T

P = 0.03 /0.179 W

P = 0.17 W

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