Problem 13.57 Part A A spring-mass oscillator consists of a mass and a spring co

Question

Problem 13.57 Part A A spring-mass oscillator consists of a mass and a spring connected as shown. The coordinate s measures the displacement of the mass relative to its position when the spring is unstretched. If the spring is linear, the mass is subjected to a deceleration proportional to s. Suppose that a =-4s m/s 2 and that you give the mass a velocity u = 0.50 m/s in the position s How far will the mass move to the right before the spring brings it to a stop? Express your answer with the appropriate units s= 1 Value Units Submit My Answers Give Up Part B 0 ? What will be the velocity of the mass when it has returned to the position s (Figure 1) Express your answer with the appropriate units Figure 1 of 1 u= 1 Value Units Submit My Answers Give Up Provide Feedback Continue

Explanation / Answer

A. v = 0.5 m/s at s = 0   
a = -4 s
dv/dt = -4 s
vdv = -4 sds
integrating both sides
v^2 = -4s^2 + C
at s = 0, v^2 = C
C = 0.25
so, v^2 + 4s^2 = 0.25
at v = 0
s = 0.25 m

B. at s = 0
v = 0.5 m/s

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