# 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?

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