.A frictionless spring of spring constant 500 N/m has one end attached to a vert
ID: 2147298 • Letter: #
Question
.A frictionless spring of spring constant 500 N/m has one end attached to a vertical wall and the other end to a block of mass 3.0 kg, which is free to move in one dimension on a horizontal frictionless table. When the spring is relaxed, the block is at x = 0. Now the block is pulled to a displacement of 20 cm and left to oscillate. Assume no friction.a. Find the amplitude and frequency of oscillation.
b. After how much time does the block first return to x = 0?
c. What is the time period of the oscillation?
d. What is the maximum Elastic Potential Energy?
Explanation / Answer
given: x = 20 cm = 0.20m a) amplitude will be 0.20 m because there is no friction in the table. Therefore, the total energy is conserved throughout the motion and thus, since the spring is pulled back by a distance of 0.20 m, the block will oscillate between x = 0.20 m and x = -0.20 m frequency = (1/2pi) sqrt(k/m) frequency = (1/2pi) sqrt(500/3) frequency = 2.05 Hz b) We can determine the period (the time it takes for the object to return back to x = 0.20 m) can be determined by: Period = 1/frequency Period = 1/2.05 Period = 0.487 s By definition of waves, the object will reach the equilibrium state (x = 0) in 1/4 of the period: t = 0.25(0.487) t = .122 s c) As stated in part b, the period is 0.487 s d) PE = (0.5)kA^2 PE = 0.5(500)(0.20)^2 PE = 10 J BOL
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