Problem 24: A spring with stiffness constant k = 5 N/m, lies horizontally on fri

Question

Problem 24: A spring with stiffness constant k = 5 N/m, lies horizontally on frictionless table One end of the spring is attached to a block of mass m = 0.2 kg and the other end is attached to a wall. The relaxed length of the spring is L,-1.0 m You pull the block to the right along the positive x-axis, so that the length of the spring is now L = 1.2 m At this instant of time (1-0 you gently release the block. What is the velocity ofthe block at time step = 0.1 s after it is released? 0 1n7 A) 0.1 m/s B) 0.2 m/s C) 0.3 m/s D) 0.4 m/s E) 0.5 m/s

Explanation / Answer

m = mass of block attached = 0.2 kg

k = spring constant = 5 N/m

w = angular frequency

angular frequency is given as

w = sqrt(k/m) = sqrt(5/0.2) = 5 rad/s

A = amplitude of oscillation = L - Lo = 1.2 - 1 = 0.2 m

Position at any time is given as

x = A Coswt

velocity is given as

v = dx/dt = - Aw Sinwt

v = - (0.2 x 5) Sin(5 x 0.1)

v = - 0.5 m/s  

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.