a 5.2 kg object on a frictionless horizontal surface is attached to one end of a

Question

a 5.2 kg object on a frictionless horizontal surface is attached to one end of a horizontal spring that has a force content k=718N/m. the spring is stretched 7.9 cm from equilibrium and released.
1)what is the frequency of the motion? 2)what is the period of the motion? 3)what is the amplitude of the motion? 4)what is the maximum speed of the motion? 5)what is the maximum acceleration of the motion? 6)when does the object first reach its equilibrium position? 7)what is its acceleration at this time? a 5.2 kg object on a frictionless horizontal surface is attached to one end of a horizontal spring that has a force content k=718N/m. the spring is stretched 7.9 cm from equilibrium and released.
1)what is the frequency of the motion? 2)what is the period of the motion? 3)what is the amplitude of the motion? 4)what is the maximum speed of the motion? 5)what is the maximum acceleration of the motion? 6)when does the object first reach its equilibrium position? 7)what is its acceleration at this time?
1)what is the frequency of the motion? 2)what is the period of the motion? 3)what is the amplitude of the motion? 4)what is the maximum speed of the motion? 5)what is the maximum acceleration of the motion? 6)when does the object first reach its equilibrium position? 7)what is its acceleration at this time?

Explanation / Answer

a)

frequency

f=(1/2pi)*sqrt[K/m]=(1/2pi)*sqr[718/5.2]

f=1.87 Hz

b)

T=1/1.87=0.5347 s

c)

A=7.9 cm

d)

W=sqrt[K/m]=sqrt[718/5.2]=11.75 rad/s

Vmax=AW=0.079*11.75

Vmax=0.9283 m/s

e)

amax=AW2=0.079*11.752

amax=10.91 m/s2

f)

X=ACos(Wt)

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

since W=2pif

t=pi/4pi*f = 1/4f =T/4 =0.5347/4

t=0.1337 s

h)

a=0 m/s2

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