A given spring stretches 0.1m when a force of 20N pulls on it . A 2 kg block attached to  it on a frictionless surface pulled on the right 0.2 m and released .

a.  What is the frequency of oscillation of block?

b.  what is the velocity of the midpoint ?

c.  what is its acceleration at either end?

d.  what is the acceleration and velocity when x=0.12m on the block’s first passing this point?

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solution

The spring attached(x)=0.1 m

force (f)= 20 N

mass of block(m)=2 kg

distance toward right (r)=0.2 m

frequency of oscillation of block (f)=?

velocity and accleration when x=0.12 on the spring block =?

we have ,

f=kx

k=f/x= 20/0.1 =200 n/m

a. frequency (f)= \(\frac{1}{2\pi}\sqrt{\frac{k}{m}}\)

=\(\frac{1}{2\pi}\sqrt{\frac{200}{2}}\)

=1.6 Hz

velocity when x=0.12m pasing this point,

v=ω\(\sqrt{r^2-x^2}\)

=2\(\pi)\)*f\(\sqrt{0.2^2-0.12^2}\)

=1.6 m\sec2

accleration (a)=ω2x

=(2\(\pi)\)*1.6)2*0.12

=12.12 m\sec2

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