A 5.4-kg object on a frictionless horizontal surface is attached to one end of a

Question

A 5.4-kg object on a frictionless horizontal surface is attached to one end of a horizontal spring that has a force constantk = 768 N/m. The spring is stretched 8.8 cm from equilibrium and released.

1)

(a) What is the frequency of the motion?
Hz

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2)

(b) What is the period of the motion?
s

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3)

(c) What is the amplitude of the motion?
cm

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4)

(d) What is the maximum speed of the motion?
m/s

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5)

(e) What is the maximum acceleration of the motion?
m/s2

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6)

(f) When does the object first reach its equilibrium position?
s

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7)

(h) What is its acceleration at this time?

m/s2

Explanation / Answer

a)

frequency

f=(1/2pi)*sqrt[K/m]=(1/2pi)*sqr[768/5.4]

f=1.9Hz

b)

T=1/1.9 =0.527 s

c)

A=8.8 cm

d)

W=sqrt[K/m]=sqrt[768/5.4]=11.9 rad/s

Vmax=AW=0.088*11.9

Vmax=1.05 m/s

e)

amax=AW2=0.088*11.92

amax=12.5 m/s2

f)

X=ACos(Wt)

Wt=Cos-1(0)=pi/2

since W=2pif

t=pi/4pi*f = 1/4f =T/4 =0.527/4

t=0.132 s

h)

a=0 m/s2

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