A 1.00-kg glider attached to a spring with a force constant 49.0 Nm oscillates o

Question

A 1.00-kg glider attached to a spring with a force constant 49.0 Nm oscillates on a frictionless, horizontal air track. At t 0, the glider is released from rest at x -3.40 cm (that is, the spring is compressed by 340 cm). (a) Find the period of the glder's motion. (b) Find the maximum values of its speed and acceleration. m/s2 (c) Find the position, velocity, and acceleration as functions of time. (where position is in m, velocity is in m/s, acceleration is in m/s, and t is in s. use the following as necessary: t) x(t) v(t) a(t) Need Help? LRendit

Explanation / Answer

part a)

m=1 kg

k=49 N/m , x=-3.4 cm=0.034 m

F=- kx= 49 * 0,034=1.66 N

T=2m/k

T=2 * 3.14 1/49

T=2 * 3.14/7

T=0.8971 sec

part b

maximum velocity= w * A

w=k/m=49/1=7

max vel=7*0.034=0.238 m/s

maximum acceleration=w2A

maximum acceleration=7 * 7* 0.034=1.666 m/s2

part c)

x(t) = Acos(t + ) = 0.034cos(wt + ) = -0.034cos(7t),
v(t) = -Asin(t + ) = 0.238sin(7t),
a(t) = -2Acos(t + ) =1.666 cos(7t).

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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